Journal of Knot Theory and its Ramifications Short Title: J. Knot Theory Ramifications Publisher: World Scientific, Singapore ISSN: 0218-2165; 1793-6527/e Online: https://www.worldscientific.com/loi/jktr Comments: Journal; Indexed cover-to-cover Documents Indexed: 2,707 Publications (since 1992) References Indexed: 2,359 Publications with 34,586 References. all top 5 Latest Issues 32, No. 9 (2023) 32, No. 8 (2023) 32, No. 7 (2023) 32, No. 6 (2023) 32, No. 5 (2023) 32, No. 4 (2023) 32, No. 3 (2023) 32, No. 2 (2023) 32, No. 1 (2023) 31, No. 14 (2022) 31, No. 13 (2022) 31, No. 12 (2022) 31, No. 11 (2022) 31, No. 10 (2022) 31, No. 9 (2022) 31, No. 8 (2022) 31, No. 7 (2022) 31, No. 6 (2022) 31, No. 5 (2022) 31, No. 4 (2022) 31, No. 3 (2022) 31, No. 2 (2022) 31, No. 1 (2022) 30, No. 14 (2021) 30, No. 13 (2021) 30, No. 12 (2021) 30, No. 11 (2021) 30, No. 10 (2021) 30, No. 9 (2021) 30, No. 8 (2021) 30, No. 7 (2021) 30, No. 6 (2021) 30, No. 5 (2021) 30, No. 4 (2021) 30, No. 3 (2021) 30, No. 2 (2021) 30, No. 1 (2021) 29, No. 14 (2020) 29, No. 13 (2020) 29, No. 12 (2020) 29, No. 11 (2020) 29, No. 10 (2020) 29, No. 9 (2020) 29, No. 8 (2020) 29, No. 7 (2020) 29, No. 6 (2020) 29, No. 5 (2020) 29, No. 4 (2020) 29, No. 3 (2020) 29, No. 2 (2020) 29, No. 1 (2020) 28, No. 14 (2019) 28, No. 13 (2019) 28, No. 12 (2019) 28, No. 11 (2019) 28, No. 10 (2019) 28, No. 9 (2019) 28, No. 8 (2019) 28, No. 7 (2019) 28, No. 6 (2019) 28, No. 5 (2019) 28, No. 4 (2019) 28, No. 3 (2019) 28, No. 2 (2019) 28, No. 1 (2019) 27, No. 14 (2018) 27, No. 13 (2018) 27, No. 12 (2018) 27, No. 11 (2018) 27, No. 10 (2018) 27, No. 9 (2018) 27, No. 8 (2018) 27, No. 7 (2018) 27, No. 6 (2018) 27, No. 5 (2018) 27, No. 4 (2018) 27, No. 3 (2018) 27, No. 2 (2018) 27, No. 1 (2018) 26, No. 14 (2017) 26, No. 13 (2017) 26, No. 12 (2017) 26, No. 11 (2017) 26, No. 10 (2017) 26, No. 9 (2017) 26, No. 8 (2017) 26, No. 7 (2017) 26, No. 6 (2017) 26, No. 5 (2017) 26, No. 4 (2017) 26, No. 3 (2017) 26, No. 2 (2017) 26, No. 1 (2017) 25, No. 14 (2016) 25, No. 13 (2016) 25, No. 12 (2016) 25, No. 11 (2016) 25, No. 10 (2016) 25, No. 9 (2016) 25, No. 8 (2016) ...and 221 more Volumes all top 5 Authors 73 Kauffman, Louis Hirsch 48 Manturov, Vassiliĭ Olegovich 37 Nelson, Sam 27 Przytycki, Józef Henryk 25 Lee, Sang Youl 24 Lambropoulou, Sofia S. F. 24 Nakanishi, Yasutaka 24 Saito, Masahico 23 Diao, Yuanan 23 Kawauchi, Akio 23 Silver, Daniel S. 22 Kanenobu, Taizo 21 Kamada, Seiichi 21 Williams, Susan G. 20 Ernst, Claus 20 Jin, Gyo Taek 19 Bae, Yongju 19 Ohyama, Yoshiyuki 17 Hoste, Jim 17 Oh, Seungsang 17 Taniyama, Kouki 16 Adams, Colin C. 16 Im, Young Ho 16 Jablan, Slavik Vlado 16 Traldi, Lorenzo 15 Jeong, Myeong-Ju 15 Mellor, Blake 15 Satoh, Shin 15 Sazdanović, Radmila 15 Teragaito, Masakazu 14 Carter, J. Scott 14 Hillman, Jonathan Arthur 14 Ogasa, Eiji 14 Ozawa, Makoto 14 Shimizu, Ayaka 14 Yetter, David N. 13 Ito, Noboru 13 Kamada, Naoko 13 Lei, Fengchun 12 Cheng, Zhiyun 12 Jin, Xian’an 12 Kadokami, Teruhisa 12 Lee, Hwa Jeong 12 Lee, Sangyop 12 Montesinos-Amilibia, José María 12 Nakamura, Takuji 11 Bardakov, Valeriĭ Georgievich 11 Dye, Heather Ann 11 Elhamdadi, Mohamed 11 Hayashi, Chuichiro 11 Kim, Sera 11 Lee, Junghoon 11 Lopes, Pedro 11 Miyazawa, Yasuyuki 11 Nikkuni, Ryo 11 Nikonov, Igor Mikhailovich 11 Shanahan, Patrick D. 11 Yang, Zhiqing 10 Dabkowski, Mieczysław K. 10 Huh, Youngsik 10 Kim, Jieon 10 Morton, Hugh R. 10 Takioka, Hideo 10 Tran, Anh Tuan 9 Birman, Joan S. 9 Fenn, Roger A. 9 Henrich, Allison K. 9 Horiuchi, Sumiko 9 Kim, Joonoh 9 Kim, Seongjeong 9 Lee, Kyeonghui 9 Lozano, María Teresa 9 No, Sungjong 9 Vesnin, Andrei Yu. 9 Yasuhara, Akira 8 Bar-Natan, Dror 8 Bartholomew, Andrew 8 Caprau, Carmen Livia 8 Chmutov, Sergei V. 8 Chrisman, Micah Whitney 8 Frohman, Charles D. 8 Garoufalidis, Stavros 8 Gordon, Cameron McA. 8 Hilden, Hugh Michael 8 Hsieh, Chun-Chung 8 Ichihara, Kazuhiro 8 Ito, Tetsuya 8 Janse van Rensburg, Esaias J. 8 Kalfagianni, Efstratia 8 Millett, Kenneth C. 8 Park, Chan-Young 8 Seo, Myoungsoo 8 Shibuya, Tetsuo 8 Stoimenow, Alexander 8 Tanaka, Toshifumi 8 Tsukamoto, Tatsuya 7 Bellingeri, Paolo 7 Brittenham, Mark 7 Eudave-Muñoz, Mario 7 Fleming, Thomas R. ...and 1,985 more Authors all top 5 Fields 2,596 Manifolds and cell complexes (57-XX) 275 Group theory and generalizations (20-XX) 181 Combinatorics (05-XX) 87 Quantum theory (81-XX) 71 Algebraic topology (55-XX) 59 Differential geometry (53-XX) 55 Nonassociative rings and algebras (17-XX) 51 Associative rings and algebras (16-XX) 45 Category theory; homological algebra (18-XX) 40 Algebraic geometry (14-XX) 31 Biology and other natural sciences (92-XX) 28 Dynamical systems and ergodic theory (37-XX) 27 General and overarching topics; collections (00-XX) 27 Global analysis, analysis on manifolds (58-XX) 24 Number theory (11-XX) 24 Computer science (68-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 History and biography (01-XX) 14 Geometry (51-XX) 14 Probability theory and stochastic processes (60-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Convex and discrete geometry (52-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 7 Commutative algebra (13-XX) 7 Functional analysis (46-XX) 7 General topology (54-XX) 6 Mathematical logic and foundations (03-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Topological groups, Lie groups (22-XX) 6 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 5 Special functions (33-XX) 5 Relativity and gravitational theory (83-XX) 4 General algebraic systems (08-XX) 3 Approximations and expansions (41-XX) 3 Optics, electromagnetic theory (78-XX) 2 Field theory and polynomials (12-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 \(K\)-theory (19-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 1,948 Publications have been cited 12,019 times in 5,877 Documents Cited by ▼ Year ▼ Racks and links in codimension two. Zbl 0787.57003Fenn, Roger; Rourke, Colin 216 1992 Abstract link diagrams and virtual knots. Zbl 0997.57018Kamada, Naoko; Kamada, Seiichi 137 2000 Stable equivalence of knots on surfaces and virtual knot cobordisms. Zbl 1004.57007Carter, J. Scott; Kamada, Seiichi; Saito, Masahico 133 2002 Temperley-Lieb algebras for non-planar statistical mechanics. – The partition algebra construction. Zbl 0804.16002Martin, Paul 104 1994 On the invariants of torus knots derived from quantum groups. Zbl 0787.57006Rosso, Marc; Jones, Vaughan 71 1993 Two-dimensional topological quantum field theories and Frobenius algebras. Zbl 0897.57015Abrams, Lowell 70 1996 Fast Khovanov homology computations. Zbl 1234.57013Bar-Natan, Dror 68 2007 BPS spectra and 3-manifold invariants. Zbl 1448.57020Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun 66 2020 Geometric interpretations of quandle homology. Zbl 1002.57019Carter, J. Scott; Kamada, Seiichi; Saito, Masahico 64 2001 Virtual crossing number and the arrow polynomial. Zbl 1195.57028Dye, H. A.; Kauffman, Louis H. 60 2009 A sequence of degree one Vassiliev invariants for virtual knots. Zbl 1195.57030Henrich, Allison 57 2010 Notions of positivity and the Ozsváth-Szabó concordance invariant. Zbl 1195.57029Hedden, Matthew 56 2010 The skein method for three-manifold invariants. Zbl 0793.57003Lickorish, W. B. R. 56 1993 Surfaces in \(R^ 4\) of braid index three are ribbon. Zbl 0763.57013Kamada, Seiichi 50 1992 Unknotting virtual knots with Gauss diagram forbidden moves. Zbl 0997.57016Nelson, Sam 49 2001 Virtual knot presentation of ribbon torus-knots. Zbl 0997.57037Satoh, Shin 49 2000 Perturbative Chern-Simons theory. Zbl 0861.57009Bar-Natan, Dror 48 1995 Alexander groups and virtual links. Zbl 0997.57019Silver, Daniel S.; Williams, Susan G. 47 2001 State-sum invariants of 4-manifolds. Zbl 0883.57021Crane, Louis; Kauffman, Louis H.; Yetter, David N. 46 1997 An affine index polynomial invariant of virtual knots. Zbl 1271.57040Kauffman, Louis H. 46 2013 Invariants of colored links. Zbl 0758.57004Akutsu, Yasuhiro; Deguchi, Tetsuo; Ohtsuki, Tomotada 44 1992 On homology of virtual braids and Burau representation. Zbl 0997.57020Vershinin, Vladimir V. 43 2001 Categorifications of the colored Jones polynomial. Zbl 1083.57019Khovanov, Mikhail 43 2005 A formula for the A-polynomial of twist knots. Zbl 1057.57010Hoste, Jim; Shanahan, Patrick D. 43 2004 Link polynomials and a graphical calculus. Zbl 0795.57001Kauffman, Louis H.; Vogel, Pierre 42 1992 Forbidden moves unknot a virtual knot. Zbl 0997.57015Kanenobu, Taizo 42 2001 Invariants of 3-manifolds derived from finite dimensional Hopf algebras. Zbl 0843.57007Kauffman, Louis H.; Radford, David E. 42 1995 Extraspecial 2-groups and images of braid group representations. Zbl 1097.20034Franko, Jennifer M.; Rowell, Eric C.; Wang, Zhenghan 42 2006 Vassiliev homotopy string link invariants. Zbl 0878.57003Bar-Natan, Dror 41 1995 Rasmussen invariant, slice-Bennequin inequality, and sliceness of knots. Zbl 1148.57011Shumakovitch, Alexander N. 41 2007 Reidemeister moves for surface isotopies and their interpretation as moves to movies. Zbl 0808.57020Carter, J. Scott; Saito, Masahico 40 1993 A polynomial invariant of virtual links. Zbl 1284.57005Cheng, Zhiyun; Gao, Hongzhu 37 2013 Virtual braids and the \(L\)-move. Zbl 1105.57002Kauffman, Louis H.; Lambropoulou, Sofia 36 2006 Understanding the Kauffman bracket skein module. Zbl 0932.57015Bullock, Doug; Frohman, Charles; Kania-Bartoszyńska, Joanna 36 1999 The \((2,\infty)\)-skein module of lens spaces; a generalization of the Jones polynomial. Zbl 0796.57005Hoste, Jim; Przytycki, Józef H. 36 1993 Introduction to virtual knot theory. Zbl 1255.57005Kauffman, Louis H. 36 2012 A multi-variable polynomial invariant for virtual knots and links. Zbl 1171.57006Miyazawa, Yasuyuki 35 2008 An invariant for singular knots. Zbl 1188.57010Juyumaya, J.; Lambropoulou, S. 35 2009 Finite type invariants of integral homology 3-spheres. Zbl 0942.57009Ohtsuki, Tomotada 35 1996 A note on non-classical virtual knots. Zbl 1094.57012Kishino, Toshimasa; Satoh, Shin 35 2004 Index polynomial invariant of virtual links. Zbl 1201.57005Im, Young Ho; Lee, Kyeonghui; Lee, Sang Youl 34 2010 A survey on Heegaard Floer homology and concordance. Zbl 1360.57002Hom, Jennifer 34 2017 Enumeration of chord diagrams and an upper bound for Vassiliev invariants. Zbl 0892.57003Stoimenow, A. 33 1998 Extensions of quandles and cocycle knot invariants. Zbl 1049.57008Carter, J. Scott; Elhamdadi, Mohamed; Nikiforou, Marina Appiou; Saito, Masahico 33 2003 Colored HOMFLY polynomials from Chern-Simons theory. Zbl 1296.57015Nawata, Satoshi; Ramadevi, P.; Zodinmawia 32 2013 Knot theory related to generalized and cyclotomic Hecke algebras of type \({\mathcal B}\). Zbl 0933.57007Lambropoulou, Sofia 31 1999 On the Casson knot invariant. Zbl 0997.57021Polyak, Michael; Viro, Oleg 31 2001 Invariants of knot diagrams and relations among Reidemeister moves. Zbl 0998.57021Östlund, Olof-Petter 31 2001 Quaternionic invariants of virtual knots and links. Zbl 1149.57301Bartholomew, Andrew; Fenn, Roger 31 2008 Distinguishing mutants by knot polynomials. Zbl 0866.57002Morton, Hugh R.; Cromwell, Peter R. 31 1996 Idempotents of Hecke algebras of type \(A\). Zbl 0924.57005Aiston, A. K.; Morton, H. R. 31 1998 Minimal knotted polygons on the cubic lattice. Zbl 0797.57004Diao, Yuanan 30 1993 Magnetic graphs and an invariant for virtual links. Zbl 1116.57008Miyazawa, Yasuyuki 29 2006 On a calculus for 2-knots and surfaces in 4-space. Zbl 1001.57044Swenton, Frank J. 28 2001 A new point of view in the theory of knot and link invariants. Zbl 1002.57026Labastida, José M. F.; Mariño, Marcos 28 2002 Remarks on the \(A\)-polynomial of a knot. Zbl 0890.57012Cooper, D.; Long, D. D. 28 1996 Boundedness and regularizing effects of O’Hara’s knot energies. Zbl 1238.57007Blatt, Simon 28 2012 Calculating Bar-Natan’s characteristic two Khovanov homology. Zbl 1114.57015Turner, Paul R. 27 2006 Generalized Temperley-Lieb algebras and decorated tangles. Zbl 0926.20005Green, R. M. 27 1998 TQFT’s from homotopy 2-types. Zbl 0787.57002Yetter, David N. 27 1993 Stick numbers and composition of knots and links. Zbl 0884.57005Adams, Colin C.; Brennan, Bevin M.; Greilsheimer, Deborah L.; Woo, Alexander K. 27 1997 Khovanov homology, Lee homology and a Rasmussen invariant for virtual knots. Zbl 1380.57012Dye, Heather A.; Kaestner, Aaron; Kauffman, Louis H. 27 2017 Markov theorem for transversal links. Zbl 1046.57007Orevkov, S. Yu.; Shevchishin, V. V. 27 2003 The simplest hyperbolic knots. Zbl 0933.57010Callahan, Patrick J.; Dean, John C.; Weeks, Jeffrey R. 26 1999 The Gordian complex of knots. Zbl 1004.57008Hirasawa, Mikami; Uchida, Yoshiaki 26 2002 Generalized spin models. Zbl 0842.57010Kawagoe, Kenichi; Munemasa, Akihiro; Watatani, Yasuo 26 1994 The knotting of equilateral polygons in \(\mathbb{R}^ 3\). Zbl 0846.57004Diao, Yuanan 26 1995 Polygon indices and superbridge indices of torus knots and links. Zbl 0881.57002Jin, Gyo Taek 26 1997 An oriented model for Khovanov homology. Zbl 1195.57024Blanchet, Christian 26 2010 Markov trace on the Yokonuma-Hecke algebra. Zbl 1100.20008Juyumaya, J. 26 2004 Hopfological algebra and categorification at a root of unity: the first steps. Zbl 1370.18017Khovanov, Mikhail 26 2016 Gauss’ linking number revisited. Zbl 1230.57009Ricca, Renzo L.; Nipoti, Bernardo 25 2011 On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant. Zbl 0844.57006Hilden, Hugh M.; Lozano, Maria Teresa; Montesinos-Amilibia, Jose Maria 25 1995 On random knots. Zbl 0846.57003Diao, Yuanan; Pippenger, Nicholas; Sumners, De Witt 25 1994 Detecting non-triviality of virtual links. Zbl 1049.57006Kadokami, Teruhisa 25 2003 Geometric knot spaces and polygonal isotopy. Zbl 1001.57024Calvo, Jorge Alberto 24 2001 Quandle colorings of knots and applications. Zbl 1302.57016Clark, W. Edwin; Elhamdadi, Mohamed; Saito, Masahico; Yeatman, Timothy 24 2014 Topological quantum field theories associated to finite groups and crossed \(G\)-sets. Zbl 0770.57010Yetter, David N. 23 1992 Quantum groups at roots of unity and modularity. Zbl 1117.17006Sawin, Stephen F. 23 2006 Trace fields of twist knots. Zbl 1003.57014Hoste, Jim; Shanahan, Patrick D. 23 2001 The noncommutative A-ideal of a \((2,2p+1)\)-torus knot determines its Jones polynomial. Zbl 1034.57005Gelca, Răzvan; Sain, Jeremy 23 2003 Triple crossing number of knots and links. Zbl 1270.57014Adams, Colin 23 2013 On the complex volume of hyperbolic knots. Zbl 1226.57025Yokota, Yoshiyuki 22 2011 Vassiliev knot invariants coming from Lie algebras and 4-invariants. Zbl 0998.57034Soboleva, E. 22 2001 Thistlethwaite’s theorem for virtual links. Zbl 1163.57001Chmutov, Sergei; Voltz, Jeremy 22 2008 Singular braids and Markov’s theorem. Zbl 0885.57005Gemein, Bernd 22 1997 Colored ribbon Hopf algebras and universal invariants of framed links. Zbl 0798.57006Ohtsuki, Tomotada 22 1993 The planarity problem for signed Gauss words. Zbl 0821.57010Cairns, Grant; Elton, Daniel M. 22 1993 Braids, orderings and zero divisors. Zbl 0928.20031Rolfsen, Dale; Zhu, Jun 22 1998 Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks. Zbl 1443.16040Bachiller, David 22 2018 Topological properties of cyclically presented groups. Zbl 1031.57002Cavicchioli, Alberto; Repovš, Dušan; Spaggiari, Fulvia 22 2003 Parity and projection from virtual knots to classical knots. Zbl 1280.57007Manturov, Vassily Olegovich 22 2013 On the classification of quandles of low order. Zbl 1333.57026Vendramin, L. 22 2012 A table of genus two handlebody-knots up to six crossings. Zbl 1236.57015Ishii, Atsushi; Kishimoto, Kengo; Moriuchi, Hiromasa; Suzuki, Masaaki 22 2012 The singular baid monoid embeds in a group. Zbl 0971.57011Fenn, Roger; Keyman, Ebru; Rourke, Colin 22 1998 The genus of closed 3-braids. Zbl 0773.57007Xu, Peijun 21 1992 Kauffman monoids. Zbl 1025.57015Borisavljević, Mirjana; Došen, Kosta; Petrić, Zoran 21 2002 A spanning tree model for Khovanov homology. Zbl 1167.57006Wehrli, S. 21 2008 Braids and the Nielsen-Thurston classification. Zbl 0874.57010Bernardete, Diego; Nitecki, Zbigniew; Gutierrez, Mauricio 21 1995 Ribbon abelian categories as modular categories. Zbl 0936.18011Lyubashenko, V. 21 1996 Refined large \(N\) duality for knots. Zbl 07708675Kameyama, Masaya; Nawata, Satoshi 5 2023 Arithmetic Chern-Simons theory with real places. Zbl 07685364Lee, Jungin; Park, Jeehoon 1 2023 Fundamental heap for framed links and ribbon cocycle invariants. Zbl 07694981Saito, Masahico; Zappala, Emanuele 1 2023 The average genus of oriented rational links with a given crossing number. Zbl 1518.57011Ray, Dawn; Diao, Yuanan 1 2023 Parity on based matrices. Zbl 07527792Nikonov, Igor 2 2022 Torus knots obtained by negatively twisting torus knots. Zbl 1487.57010Lee, Sangyop; de Paiva, Thiago 2 2022 Bicategories for TQFTs with defects with structure. Zbl 1501.57025Lee, I. J.; Yetter, D. N. 2 2022 Ribbonlength of twisted torus knots. Zbl 1504.57008Kim, Hyoungjun; No, Sungjong; Yoo, Hyungkee 2 2022 Hyperbolicity of augmented links in the thickened torus. Zbl 07550881Kwon, Alice; Tham, Ying Hong 2 2022 The quantum trace as a quantum non-abelianization map. Zbl 07566140Korinman, J.; Quesney, A. 2 2022 Twisted virtual bikeigebras and twisted virtual handlebody-knots. Zbl 1497.57012Nelson, Sam; Zhao, Yuqi 1 2022 The minimum number of coloring of knots. Zbl 1490.57003Han, Youfa; Zhou, Boxin 1 2022 On linear resolvability of universal quantum dimensions. Zbl 1502.17011Avetisyan, M. Y.; Mkrtchyan, R. L. 1 2022 An Alexander-type invariant for doodles. Zbl 1515.57013Cisneros, Bruno; Flores, Marcelo; Juyumaya, Jesús; Roque-Márquez, Christopher 1 2022 Families of curly knots. Zbl 1516.57006Ernst, C.; Gover, S. 1 2022 The Rohlin invariant and \(\mathbb{Z}/2\)-valued invariants of homology spheres. Zbl 1498.57018Riba, Ricard 1 2022 Peripheral elements in reduced Alexander modules. Zbl 1511.57009Traldi, Lorenzo 1 2022 On universal parity on free two-dimensional knots. Zbl 1511.57016Nikonov, Igor 1 2022 Almost all strongly quasipositive braid closures are fibered. Zbl 07619471Banfield, Ian M. 1 2022 Reducible surgery in lens spaces and seiferters. Zbl 1510.57004Gainullin, Fyodor 1 2022 The smooth 4-genus of (the rest of) the prime knots through 12 crossings. Zbl 1505.57005Brittenham, Mark; Hermiller, Susan 1 2022 A Möbius invariant discretization of O’Hara’s Möbius energy. Zbl 1496.57004Blatt, Simon; Ishizeki, Aya; Nagasawa, Takeyuki 1 2022 All prime knots through 10 crossings have superbridge index \(\leq 5\). Zbl 1494.57011Shonkwiler, Clayton 1 2022 Crosscap number three alternating knots. Zbl 1497.57005Ito, Noboru; Takimura, Yusuke 1 2022 The non-orientable 4-genus for knots with 10 crossings. Zbl 1493.57002Ghanbarian, Nakisa 1 2022 Alternating odd pretzel knots and chirally cosmetic surgeries. Zbl 1503.57004Varvarezos, Konstantinos 1 2022 A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu 5 2021 Polynomial invariants of singular knots and links. Zbl 1464.57009Ceniceros, Jose; Churchill, Indu R.; Elhamdadi, Mohamed 4 2021 Torsion in Khovanov homology of homologically thin knots. Zbl 1490.57012Shumakovitch, Alexander N. 4 2021 Fixing the functoriality of Khovanov homology: a simple approach. Zbl 07478463Sano, Taketo 3 2021 Symmetric union presentations for 2-bridge ribbon knots. Zbl 1486.57011Lamm, Christoph 3 2021 On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere. Zbl 1490.57018Bakshi, Rhea Palak; Mukherjee, Sujoy; Przytycki, Józef H.; Silvero, Marithania; Wang, Xiao 3 2021 The colored Jones polynomial and Kontsevich-Zagier series for double twist knots. Zbl 1470.57023Lovejoy, Jeremy; Osburn, Robert 3 2021 Arrow diagrams on spherical curves and computations. Zbl 1476.57009Ito, Noboru; Takamura, Masashi 2 2021 Tied links in various topological settings. Zbl 1487.57004Diamantis, Ioannis 2 2021 Tied links in the solid torus. Zbl 1462.57004Flores, Marcelo 2 2021 Decompositions of the \(3\)-sphere and lens spaces with three handlebodies. Zbl 1483.57005Ito, Yasuyoshi; Ogawa, Masaki 2 2021 Knots with equal bridge index and braid index. Zbl 07478464Diao, Yuanan; Ernst, Claus; Reiter, Philipp 2 2021 The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams. Zbl 1486.57006Cohen, Moshe 2 2021 Superbridge and bridge indices for knots. Zbl 1466.57002Adams, Colin; Agarwal, Nikhil; Allen, Rachel; Khandhawit, Tirasan; Simons, Alex; Winarski, Rebecca; Wootters, Mary 2 2021 A relation between the crossing number and the height of a knotoid. Zbl 1479.57024Korablev, Philipp; Tarkaev, Vladimir 1 2021 A free-group valued invariant of free knots. Zbl 1473.57028Manturov, Vassily Olegovich 1 2021 Vertex distortion of lattice knots. Zbl 1487.57003Campisi, Marion; Cazet, Nicholas 1 2021 Linking numbers, quandles and groups. Zbl 1514.57015Traldi, Lorenzo 1 2021 On the potential functions for a link diagram. Zbl 1486.57015Yoon, Seokbeom 1 2021 Writhe-like invariants of alternating links. Zbl 1464.57001Diao, Yuanan; Pham, Van 1 2021 Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces. Zbl 1484.57007Kauffman, Louis H.; Nikonov, Igor Mikhailovich; Ogasa, Eiji 1 2021 Determining the doubly slice genera of prime knots with up to \(12\) crossings. Zbl 1479.57014Karageorghis, Lucia P.; Swenton, Frank 1 2021 On equivalence of symmetric union presentations for ribbon knots. Zbl 1483.57009Tanaka, Toshifumi 1 2021 The number of oriented rational links with a given deficiency number. Zbl 1481.57009Diao, Yuanan; Finney, Michael Lee; Ray, Dawn 1 2021 Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups. Zbl 07459708Ocampo, Oscar 1 2021 A diagrammatic presentation and its characterization of non-split compact surfaces in the \(3\)-sphere. Zbl 1481.57011Matsuzaki, Shosaku 1 2021 Local-moves on knots and products of knots. II. Zbl 1485.57020Kauffman, Louis H.; Ogasa, Eiji 1 2021 Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths. Zbl 1482.52016Abrosimov, Nikolay; Vuong, Bao 1 2021 Parity, virtual closure and minimality of knotoids. Zbl 1491.57011Gügümcü, N.; Kauffman, L. H. 1 2021 Coefficients of Catalan states without nesting and maximal number of returns. Zbl 1494.57027Dabkowski, M. K.; Merrill, A. D. 1 2021 Integral geometric orbifolds. Zbl 1521.57022Lozano, María Teresa; Montesinos-Amilibia, José María 1 2021 The second Yang-Baxter homology for the HOMFLYPT polynomial. Zbl 1490.57011Przytycki, Józef H.; Wang, Xiao 1 2021 On the virtual singular braid monoid. Zbl 07512701Caprau, Carmen; Zepeda, Sarah 1 2021 On two-bridge knots and a conjecture of Hirasawa-Murasugi. Zbl 1469.57005Chen, Wenzhao 1 2021 Quandle coloring quivers of links using dihedral quandles. Zbl 1468.57007Taniguchi, Yuta 1 2021 Unknotting operations on knots and links*. Zbl 1467.57007Shimizu, Ayaka 1 2021 The reduced Dijkgraaf-Witten invariant of twist knots in the Bloch group of a finite field. Zbl 1478.57006Karuo, Hiroaki 1 2021 Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions. Zbl 1467.57015Oshiro, Kanako; Oyamaguchi, Natsumi 1 2021 Twisted torus knots \(T(mn+m+1,mn+1,mn+m+2,-1)\) and \(T(n+1,n,2n-1,-1)\) are torus knots. Zbl 1467.57005Lee, Sangyop 1 2021 Verification of the Jones unknot conjecture up to 24 crossings. Zbl 1466.57006Tuzun, Robert E.; Sikora, Adam S. 1 2021 Group presentations for links in thickened surfaces. Zbl 1472.57008Silver, Daniel S.; Williams, Susan G. 1 2021 A lower bound on critical points of the electric potential of a knot. Zbl 1470.57017Lipton, Max 1 2021 Virtual concordance and the generalized Alexander polynomial. Zbl 1479.57021Boden, Hans U.; Chrisman, Micah 1 2021 More 1-cocycles for classical knots. Zbl 1470.57008Fiedler, Thomas 1 2021 BPS spectra and 3-manifold invariants. Zbl 1448.57020Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun 66 2020 Large color \(R\)-matrix for knot complements and strange identities. Zbl 1460.57014Park, Sunghyuk 11 2020 Picture-valued parity-biquandle bracket. Zbl 1439.57028Ilyutko, Denis P.; Manturov, Vassily O. 6 2020 Multivariate Alexander quandles. I: The module sequence of a link. Zbl 1440.57011Traldi, Lorenzo 6 2020 A note on representations of welded braid groups. Zbl 1508.20040Bellingeri, Paolo; Soulié, Arthur 6 2020 Planar pure braids on six strands. Zbl 1512.20120Mostovoy, Jacob; Roque-Márquez, Christopher 6 2020 Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves. Zbl 1458.57005Gill, Amrendra; Prabhakar, Madeti; Vesnin, Andrei 5 2020 \(\mathfrak{gl}_n\)-webs, categorification and Khovanov-Rozansky homologies. Zbl 1484.57014Tubbenhauer, Daniel 5 2020 Refined Chern-Simons theory in genus two. Zbl 1450.57010Arthamonov, S.; Shakirov, Sh. 5 2020 On Bennequin-type inequalities for links in tight contact 3-manifolds. Zbl 1450.57005Cavallo, Alberto 5 2020 A lower bound of crosscap numbers of alternating knots. Zbl 1436.57006Ito, Noboru; Takimura, Yusuke 5 2020 Khovanov homology and diagonalizable Frobenius algebras. Zbl 1434.57011Turner, Paul 5 2020 Functoriality of Khovanov homology. Zbl 1481.57020Vogel, Pierre 4 2020 Comparing nonorientable three genus and nonorientable four genus of torus knots. Zbl 1439.57016Jabuka, Stanislav; Van Cott, Cornelia A. 4 2020 Kauffman skein algebras and quantum Teichmüller spaces via factorization homology. Zbl 1471.57016Cooke, Juliet 4 2020 DNA origami and unknotted A-trails in torus graphs. Zbl 1447.05063Morse, Ada; Adkisson, William; Greene, Jessica; Perry, David; Smith, Brenna; Ellis-Monaghan, Jo; Pangborn, Greta 4 2020 A neural network approach to predicting and computing knot invariants. Zbl 1439.57015Hughes, Mark C. 3 2020 On Legendrian cobordisms and generating functions. Zbl 1441.53068Limouzineau, Maÿlis 3 2020 Knots with exactly 10 sticks. Zbl 1439.57005Blair, Ryan; Eddy, Thomas D.; Morrison, Nathaniel; Shonkwiler, Clayton 3 2020 Some remarks on the chord index. Zbl 1464.57010Cheng, Zhiyun; Gao, Hongzhu; Xu, Mengjian 3 2020 A note on coverings of virtual knots. Zbl 1478.57011Nakamura, Takuji; Nakanishi, Yasutaka; Satoh, Shin 3 2020 \(F\)-polynomials of tabulated virtual knots. Zbl 1447.57009Ivanov, Maxim; Vesnin, Andrei 3 2020 Braid index bounds ropelength from below. Zbl 1439.57009Diao, Yuanan 2 2020 The knot Floer cube of resolutions and the composition product. Zbl 1476.57018Dowlin, Nathan 2 2020 State sum invariants for flat virtual links from the chord index. Zbl 1464.57011Lee, Kyeonghui; Im, Young Ho; Kim, Sera 2 2020 On realizability of Gauss diagrams and constructions of meanders. (On realizabilty of Gauss diagrams and constructions of meanders.) Zbl 1473.57012Grinblat, Andrey; Lopatkin, Viktor 2 2020 Mapping class group representations from Drinfeld doubles of finite groups. Zbl 1448.57018Fjelstad, Jens; Fuchs, Jürgen 2 2020 Erratum to: “Multivariate Alexander quandles. II. The involutory medial quandle of a link”. Zbl 1460.57007Traldi, Lorenzo 2 2020 Some remarks on twin groups. Zbl 1508.20046Naik, Tushar K.; Nanda, Neha; Singh, Mahender 2 2020 Black holes and topological surgery. Zbl 1455.57023Antoniou, Stathis; Kauffman, Louis H.; Lambropoulou, Sofia 2 2020 ...and 1247 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,045 Authors 96 Kauffman, Louis Hirsch 64 Nelson, Sam 59 Manturov, Vassiliĭ Olegovich 48 Kamada, Seiichi 43 Saito, Masahico 40 Elhamdadi, Mohamed 40 Stoimenow, Alexander 37 Przytycki, Józef Henryk 34 Diao, Yuanan 34 Ito, Tetsuya 33 Garoufalidis, Stavros 33 Ito, Noboru 32 Morozov, Alexei Yurievich 31 Bardakov, Valeriĭ Georgievich 30 Kawauchi, Akio 30 Lambropoulou, Sofia S. F. 30 Lee, Sang Youl 30 Satoh, Shin 29 Adams, Colin C. 29 Jin, Xian’an 29 Kanenobu, Taizo 29 Oh, Seungsang 28 Carter, J. Scott 28 Mironov, Andrei D. 26 East, James 26 Ishii, Atsushi 26 Silver, Daniel S. 25 Kamada, Naoko 25 Yasuhara, Akira 24 Tran, Anh Tuan 24 Williams, Susan G. 23 Ernst, Claus 23 Nakanishi, Yasutaka 23 Oshiro, Kanako 23 Patureau-Mirand, Bertrand 23 Spaggiari, Fulvia 22 Cavicchioli, Alberto 22 Geer, Nathan 22 Ichihara, Kazuhiro 22 Im, Young Ho 22 Le, Thang Tu Quoc 22 Ozawa, Makoto 22 Traldi, Lorenzo 21 Mellor, Blake 21 Orevkov, Stepan Yur’evich 20 Boden, Hans U. 20 Chbili, Nafaa 20 Sazdanović, Radmila 19 Andersen, Jørgen Ellegaard 19 Bellingeri, Paolo 19 Mattman, Thomas W. 19 Shimizu, Ayaka 18 Cheng, Zhiyun 18 Guaschi, John 18 Gukov, Sergei 18 Jablan, Slavik Vlado 18 Jeong, Myeong-Ju 18 Motegi, Kimihiko 18 Nikkuni, Ryo 18 Ohyama, Yoshiyuki 18 Singh, Mahender 18 Vesnin, Andrei Yu. 17 Bae, Yongju 17 Frohman, Charles D. 17 Khovanov, Mikhail G. 17 Meilhan, Jean-Baptiste 17 Teragaito, Masakazu 17 Xue, Kang 16 Dehornoy, Patrick 16 Dye, Heather Ann 16 Fleming, Thomas R. 16 Jin, Gyo Taek 16 Kofman, Ilya 16 Lee, Hwa Jeong 16 Lei, Fengchun 16 Livingston, Charles 16 Nakamura, Takuji 16 Nikonov, Igor Mikhailovich 15 Baker, Kenneth L. 15 Champanerkar, Abhijit 15 Chrisman, Micah Whitney 15 Cristofori, Paola 15 Gonçalves, Daciberg Lima 15 Hoste, Jim 15 Kalfagianni, Efstratia 15 Kim, Sera 15 Lopes, Pedro 15 Martin, Paul Purdon 15 Purcell, Jessica Shepherd 15 Ramadevi, Pichai 15 Rowell, Eric C. 15 Shima, Akiko 15 Taniyama, Kouki 14 Eudave-Muñoz, Mario 14 Hajij, Mustafa 14 Hedden, Matthew 14 Huh, Youngsik 14 Kim, Jieon 14 Lauda, Aaron D. 14 Lebed, Victoria ...and 3,945 more Authors all top 5 Cited in 409 Journals 1,545 Journal of Knot Theory and its Ramifications 432 Topology and its Applications 337 Algebraic & Geometric Topology 123 Journal of Algebra 121 Transactions of the American Mathematical Society 116 Advances in Mathematics 114 Proceedings of the American Mathematical Society 103 Journal of High Energy Physics 96 Communications in Mathematical Physics 90 Geometry & Topology 86 Journal of Pure and Applied Algebra 70 Osaka Journal of Mathematics 66 International Journal of Mathematics 62 Quantum Topology 56 Geometriae Dedicata 55 Journal of Mathematical Physics 53 Mathematical Proceedings of the Cambridge Philosophical Society 48 Communications in Algebra 42 Mathematische Zeitschrift 36 Nuclear Physics. B 36 Journal of Geometry and Physics 35 European Journal of Combinatorics 34 Experimental Mathematics 34 Journal of Physics A: Mathematical and Theoretical 32 Letters in Mathematical Physics 32 Tokyo Journal of Mathematics 32 Journal of Mathematical Sciences (New York) 31 Journal of the Mathematical Society of Japan 30 Mathematische Annalen 29 Journal of Topology 27 Pacific Journal of Mathematics 26 Discrete Mathematics 26 Journal of Algebraic Combinatorics 25 Selecta Mathematica. New Series 24 Journal of Combinatorial Theory. Series A 24 International Journal of Algebra and Computation 24 Journal of Algebra and its Applications 23 Quantum Information Processing 22 Inventiones Mathematicae 21 Journal of the London Mathematical Society. Second Series 20 Duke Mathematical Journal 20 Fundamenta Mathematicae 20 Advances in Applied Mathematics 19 Bulletin of the London Mathematical Society 18 Michigan Mathematical Journal 18 The Electronic Journal of Combinatorics 18 Communications in Contemporary Mathematics 17 Chaos, Solitons and Fractals 17 The New York Journal of Mathematics 17 Algebras and Representation Theory 17 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 16 Israel Journal of Mathematics 16 Acta Mathematica Vietnamica 16 Annales de l’Institut Fourier 15 Forum Mathematicum 15 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 15 Boletín de la Sociedad Matemática Mexicana. Third Series 15 Mediterranean Journal of Mathematics 14 International Journal of Modern Physics A 14 Siberian Mathematical Journal 14 Discrete & Computational Geometry 14 Proceedings of the Steklov Institute of Mathematics 13 Bulletin of the Australian Mathematical Society 13 Bulletin of the American Mathematical Society. New Series 13 Annales Henri Poincaré 13 Journal of the Australian Mathematical Society 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Journal of Topology and Analysis 13 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 12 Glasgow Mathematical Journal 12 Manuscripta Mathematica 12 Winter Braids Lecture Notes 11 Theoretical and Mathematical Physics 11 Compositio Mathematica 11 Journal für die Reine und Angewandte Mathematik 11 Acta Mathematica Sinica. English Series 11 Involve 10 Kyungpook Mathematical Journal 10 Journal of Symbolic Computation 10 Groups, Geometry, and Dynamics 9 Discrete Applied Mathematics 9 Journal of Statistical Physics 9 Mathematical Notes 9 Reviews in Mathematical Physics 9 Canadian Mathematical Bulletin 9 Indiana University Mathematics Journal 9 Journal of Graph Theory 9 Proceedings of the Edinburgh Mathematical Society. Series II 9 Semigroup Forum 9 Applied Categorical Structures 9 Journal of the European Mathematical Society (JEMS) 9 Sibirskie Èlektronnye Matematicheskie Izvestiya 9 Research in the Mathematical Sciences 9 Arnold Mathematical Journal 9 European Journal of Mathematics 8 Applied Mathematics and Computation 8 Journal of Combinatorial Theory. Series B 8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 8 Journal of Mathematical Chemistry 8 Doklady Mathematics ...and 309 more Journals all top 5 Cited in 60 Fields 4,556 Manifolds and cell complexes (57-XX) 965 Group theory and generalizations (20-XX) 582 Quantum theory (81-XX) 551 Combinatorics (05-XX) 377 Associative rings and algebras (16-XX) 307 Nonassociative rings and algebras (17-XX) 293 Category theory; homological algebra (18-XX) 258 Differential geometry (53-XX) 229 Algebraic geometry (14-XX) 219 Algebraic topology (55-XX) 164 Global analysis, analysis on manifolds (58-XX) 116 Dynamical systems and ergodic theory (37-XX) 115 Number theory (11-XX) 107 Computer science (68-XX) 89 Relativity and gravitational theory (83-XX) 82 Several complex variables and analytic spaces (32-XX) 82 Statistical mechanics, structure of matter (82-XX) 81 Functional analysis (46-XX) 75 Biology and other natural sciences (92-XX) 62 Order, lattices, ordered algebraic structures (06-XX) 55 Probability theory and stochastic processes (60-XX) 49 Convex and discrete geometry (52-XX) 46 Commutative algebra (13-XX) 43 Geometry (51-XX) 38 Topological groups, Lie groups (22-XX) 38 Functions of a complex variable (30-XX) 33 Special functions (33-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 31 Linear and multilinear algebra; matrix theory (15-XX) 30 General algebraic systems (08-XX) 23 Partial differential equations (35-XX) 23 Numerical analysis (65-XX) 22 Mathematical logic and foundations (03-XX) 22 General topology (54-XX) 21 History and biography (01-XX) 19 \(K\)-theory (19-XX) 17 General and overarching topics; collections (00-XX) 17 Fluid mechanics (76-XX) 14 Field theory and polynomials (12-XX) 14 Information and communication theory, circuits (94-XX) 13 Statistics (62-XX) 13 Mechanics of deformable solids (74-XX) 12 Mechanics of particles and systems (70-XX) 12 Optics, electromagnetic theory (78-XX) 11 Real functions (26-XX) 11 Measure and integration (28-XX) 9 Ordinary differential equations (34-XX) 8 Approximations and expansions (41-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Difference and functional equations (39-XX) 6 Systems theory; control (93-XX) 4 Operator theory (47-XX) 3 Abstract harmonic analysis (43-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year