## 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: Indexed cover-to-cover
 Documents Indexed: 2,590 Publications (since 1992) References Indexed: 2,244 Publications with 32,375 References.
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### Authors

 70 Kauffman, Louis Hirsch 47 Manturov, Vassiliĭ Olegovich 34 Nelson, Sam 27 Przytycki, Józef Henryk 24 Lee, Sang Youl 23 Kawauchi, Akio 23 Lambropoulou, Sofia S. F. 23 Saito, Masahico 23 Silver, Daniel S. 21 Diao, Yuanan 21 Kanenobu, Taizo 21 Nakanishi, Yasutaka 21 Williams, Susan G. 20 Ernst, Claus 20 Kamada, Seiichi 19 Bae, Yongju 19 Jin, Gyo Taek 19 Ohyama, Yoshiyuki 17 Oh, Seungsang 16 Im, Young Ho 16 Jablan, Slavik Vlado 16 Taniyama, Kouki 15 Adams, Colin C. 15 Hoste, Jim 15 Jeong, Myeong-Ju 15 Mellor, Blake 15 Teragaito, Masakazu 15 Traldi, Lorenzo 14 Carter, J. Scott 14 Hillman, Jonathan Arthur 14 Ozawa, Makoto 14 Yetter, David N. 13 Lei, Fengchun 13 Ogasa, Eiji 13 Satoh, Shin 13 Sazdanović, Radmila 13 Shimizu, Ayaka 12 Cheng, Zhiyun 12 Jin, Xian’an 12 Kamada, Naoko 12 Montesinos-Amilibia, José María 11 Bardakov, Valeriĭ Georgievich 11 Dye, Heather Ann 11 Elhamdadi, Mohamed 11 Hayashi, Chuichiro 11 Ito, Noboru 11 Kadokami, Teruhisa 11 Lee, Hwa Jeong 11 Lee, Junghoon 11 Lee, Sangyop 11 Lopes, Pedro 11 Nakamura, Takuji 10 Huh, Youngsik 10 Kim, Sera 10 Morton, Hugh R. 10 Nikkuni, Ryo 10 Shanahan, Patrick D. 10 Takioka, Hideo 10 Tran, Anh Tuan 9 Dabkowski, Mieczysław K. 9 Fenn, Roger A. 9 Henrich, Allison K. 9 Horiuchi, Sumiko 9 Lozano, María Teresa 9 Miyazawa, Yasuyuki 9 Vesnin, Andrei Yu. 9 Yang, Zhiqing 9 Yasuhara, Akira 8 Bartholomew, Andrew 8 Birman, Joan S. 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 Janse van Rensburg, Esaias J. 8 Kalfagianni, Efstratia 8 Kim, Jieon 8 Kim, Seongjeong 8 Millett, Kenneth C. 8 Nikonov, Igor Mikhailovich 8 Park, Chan-Young 8 Seo, Myoungsoo 8 Shibuya, Tetsuo 8 Stoimenow, Alexander 8 Tanaka, Toshifumi 8 Tsukamoto, Tatsuya 7 Bar-Natan, Dror 7 Bellingeri, Paolo 7 Caprau, Carmen Livia 7 Eudave-Muñoz, Mario 7 Fleming, Thomas R. 7 Foisy, Joel Stephen 7 Ito, Tetsuya 7 Kim, Joonoh 7 Ko, Ki Hyoung 7 Kwon, Bo-Hyun ...and 1,880 more Authors
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### Fields

 2,482 Manifolds and cell complexes (57-XX) 267 Group theory and generalizations (20-XX) 170 Combinatorics (05-XX) 85 Quantum theory (81-XX) 69 Algebraic topology (55-XX) 56 Differential geometry (53-XX) 53 Nonassociative rings and algebras (17-XX) 49 Associative rings and algebras (16-XX) 43 Category theory; homological algebra (18-XX) 39 Algebraic geometry (14-XX) 31 Biology and other natural sciences (92-XX) 28 Dynamical systems and ergodic theory (37-XX) 27 Global analysis, analysis on manifolds (58-XX) 26 General and overarching topics; collections (00-XX) 23 Number theory (11-XX) 21 Computer science (68-XX) 19 Statistical mechanics, structure of matter (82-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 15 History and biography (01-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) 12 Geometry (51-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 7 Mathematical logic and foundations (03-XX) 7 Commutative algebra (13-XX) 7 Functional analysis (46-XX) 7 General topology (54-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 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-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 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

1,832 Publications have been cited 10,515 times in 5,238 Documents Cited by Year
Racks and links in codimension two. Zbl 0787.57003
Fenn, Roger; Rourke, Colin
1992
Abstract link diagrams and virtual knots. Zbl 0997.57018
2000
Stable equivalence of knots on surfaces and virtual knot cobordisms. Zbl 1004.57007
Carter, J. Scott; Kamada, Seiichi; Saito, Masahico
2002
Temperley-Lieb algebras for non-planar statistical mechanics. – The partition algebra construction. Zbl 0804.16002
Martin, Paul
1994
Two-dimensional topological quantum field theories and Frobenius algebras. Zbl 0897.57015
Abrams, Lowell
1996
On the invariants of torus knots derived from quantum groups. Zbl 0787.57006
Rosso, Marc; Jones, Vaughan
1993
Geometric interpretations of quandle homology. Zbl 1002.57019
Carter, J. Scott; Kamada, Seiichi; Saito, Masahico
2001
Fast Khovanov homology computations. Zbl 1234.57013
Bar-Natan, Dror
2007
Virtual crossing number and the arrow polynomial. Zbl 1195.57028
Dye, H. A.; Kauffman, Louis H.
2009
A sequence of degree one Vassiliev invariants for virtual knots. Zbl 1195.57030
Henrich, Allison
2010
Surfaces in $$R^ 4$$ of braid index three are ribbon. Zbl 0763.57013
1992
The skein method for three-manifold invariants. Zbl 0793.57003
Lickorish, W. B. R.
1993
Alexander groups and virtual links. Zbl 0997.57019
Silver, Daniel S.; Williams, Susan G.
2001
Notions of positivity and the Ozsváth-Szabó concordance invariant. Zbl 1195.57029
Hedden, Matthew
2010
Unknotting virtual knots with Gauss diagram forbidden moves. Zbl 0997.57016
Nelson, Sam
2001
Perturbative Chern-Simons theory. Zbl 0861.57009
Bar-Natan, Dror
1995
Invariants of colored links. Zbl 0758.57004
Akutsu, Yasuhiro; Deguchi, Tetsuo; Ohtsuki, Tomotada
1992
Virtual knot presentation of ribbon torus-knots. Zbl 0997.57037
Satoh, Shin
2000
Categorifications of the colored Jones polynomial. Zbl 1083.57019
Khovanov, Mikhail
2005
Link polynomials and a graphical calculus. Zbl 0795.57001
Kauffman, Louis H.; Vogel, Pierre
1992
Invariants of 3-manifolds derived from finite dimensional Hopf algebras. Zbl 0843.57007
Kauffman, Louis H.; Radford, David E.
1995
On homology of virtual braids and Burau representation. Zbl 0997.57020
2001
An affine index polynomial invariant of virtual knots. Zbl 1271.57040
Kauffman, Louis H.
2013
State-sum invariants of 4-manifolds. Zbl 0883.57021
Crane, Louis; Kauffman, Louis H.; Yetter, David N.
1997
Vassiliev homotopy string link invariants. Zbl 0878.57003
Bar-Natan, Dror
1995
Forbidden moves unknot a virtual knot. Zbl 0997.57015
Kanenobu, Taizo
2001
A formula for the A-polynomial of twist knots. Zbl 1057.57010
Hoste, Jim; Shanahan, Patrick D.
2004
Extraspecial 2-groups and images of braid group representations. Zbl 1097.20034
Franko, Jennifer M.; Rowell, Eric C.; Wang, Zhenghan
2006
Reidemeister moves for surface isotopies and their interpretation as moves to movies. Zbl 0808.57020
Carter, J. Scott; Saito, Masahico
1993
A note on non-classical virtual knots. Zbl 1094.57012
Kishino, Toshimasa; Satoh, Shin
2004
Rasmussen invariant, slice-Bennequin inequality, and sliceness of knots. Zbl 1148.57011
Shumakovitch, Alexander N.
2007
Virtual braids and the $$L$$-move. Zbl 1105.57002
Kauffman, Louis H.; Lambropoulou, Sofia
2006
BPS spectra and 3-manifold invariants. Zbl 1448.57020
Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun
2020
Finite type invariants of integral homology 3-spheres. Zbl 0942.57009
1996
Index polynomial invariant of virtual links. Zbl 1201.57005
Im, Young Ho; Lee, Kyeonghui; Lee, Sang Youl
2010
Understanding the Kauffman bracket skein module. Zbl 0932.57015
Bullock, Doug; Frohman, Charles; Kania-Bartoszyńska, Joanna
1999
A polynomial invariant of virtual links. Zbl 1284.57005
Cheng, Zhiyun; Gao, Hongzhu
2013
The $$(2,\infty)$$-skein module of lens spaces; a generalization of the Jones polynomial. Zbl 0796.57005
Hoste, Jim; Przytycki, Józef H.
1993
A multi-variable polynomial invariant for virtual knots and links. Zbl 1171.57006
Miyazawa, Yasuyuki
2008
Extensions of quandles and cocycle knot invariants. Zbl 1049.57008
Carter, J. Scott; Elhamdadi, Mohamed; Nikiforou, Marina Appiou; Saito, Masahico
2003
Introduction to virtual knot theory. Zbl 1255.57005
Kauffman, Louis H.
2012
Distinguishing mutants by knot polynomials. Zbl 0866.57002
Morton, Hugh R.; Cromwell, Peter R.
1996
Knot theory related to generalized and cyclotomic Hecke algebras of type $${\mathcal B}$$. Zbl 0933.57007
Lambropoulou, Sofia
1999
On the Casson knot invariant. Zbl 0997.57021
Polyak, Michael; Viro, Oleg
2001
Invariants of knot diagrams and relations among Reidemeister moves. Zbl 0998.57021
Östlund, Olof-Petter
2001
Colored HOMFLY polynomials from Chern-Simons theory. Zbl 1296.57015
2013
Idempotents of Hecke algebras of type $$A$$. Zbl 0924.57005
Aiston, A. K.; Morton, H. R.
1998
Quaternionic invariants of virtual knots and links. Zbl 1149.57301
Bartholomew, Andrew; Fenn, Roger
2008
Magnetic graphs and an invariant for virtual links. Zbl 1116.57008
Miyazawa, Yasuyuki
2006
Minimal knotted polygons on the cubic lattice. Zbl 0797.57004
Diao, Yuanan
1993
Generalized spin models. Zbl 0842.57010
Kawagoe, Kenichi; Munemasa, Akihiro; Watatani, Yasuo
1994
Generalized Temperley-Lieb algebras and decorated tangles. Zbl 0926.20005
Green, R. M.
1998
Stick numbers and composition of knots and links. Zbl 0884.57005
Adams, Colin C.; Brennan, Bevin M.; Greilsheimer, Deborah L.; Woo, Alexander K.
1997
Enumeration of chord diagrams and an upper bound for Vassiliev invariants. Zbl 0892.57003
Stoimenow, A.
1998
On a calculus for 2-knots and surfaces in 4-space. Zbl 1001.57044
Swenton, Frank J.
2001
An invariant for singular knots. Zbl 1188.57010
Juyumaya, J.; Lambropoulou, S.
2009
Polygon indices and superbridge indices of torus knots and links. Zbl 0881.57002
Jin, Gyo Taek
1997
On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant. Zbl 0844.57006
Hilden, Hugh M.; Lozano, Maria Teresa; Montesinos-Amilibia, Jose Maria
1995
Remarks on the $$A$$-polynomial of a knot. Zbl 0890.57012
Cooper, D.; Long, D. D.
1996
The Gordian complex of knots. Zbl 1004.57008
Hirasawa, Mikami; Uchida, Yoshiaki
2002
Detecting non-triviality of virtual links. Zbl 1049.57006
2003
Boundedness and regularizing effects of O’Hara’s knot energies. Zbl 1238.57007
Blatt, Simon
2012
Calculating Bar-Natan’s characteristic two Khovanov homology. Zbl 1114.57015
Turner, Paul R.
2006
Quandle colorings of knots and applications. Zbl 1302.57016
Clark, W. Edwin; Elhamdadi, Mohamed; Saito, Masahico; Yeatman, Timothy
2014
The noncommutative A-ideal of a $$(2,2p+1)$$-torus knot determines its Jones polynomial. Zbl 1034.57005
Gelca, Răzvan; Sain, Jeremy
2003
Topological properties of cyclically presented groups. Zbl 1031.57002
Cavicchioli, Alberto; Repovš, Dušan; Spaggiari, Fulvia
2003
Singular braids and Markov’s theorem. Zbl 0885.57005
Gemein, Bernd
1997
The planarity problem for signed Gauss words. Zbl 0821.57010
Cairns, Grant; Elton, Daniel M.
1993
The simplest hyperbolic knots. Zbl 0933.57010
Callahan, Patrick J.; Dean, John C.; Weeks, Jeffrey R.
1999
The singular baid monoid embeds in a group. Zbl 0971.57011
Fenn, Roger; Keyman, Ebru; Rourke, Colin
1998
Khovanov homology, Lee homology and a Rasmussen invariant for virtual knots. Zbl 1380.57012
Dye, Heather A.; Kaestner, Aaron; Kauffman, Louis H.
2017
On the classification of quandles of low order. Zbl 1333.57026
Vendramin, L.
2012
Topological quantum field theories associated to finite groups and crossed $$G$$-sets. Zbl 0770.57010
Yetter, David N.
1992
Braids and the Nielsen-Thurston classification. Zbl 0874.57010
Bernardete, Diego; Nitecki, Zbigniew; Gutierrez, Mauricio
1995
On the complex volume of hyperbolic knots. Zbl 1226.57025
Yokota, Yoshiyuki
2011
Braids, orderings and zero divisors. Zbl 0928.20031
Rolfsen, Dale; Zhu, Jun
1998
Vassiliev knot invariants coming from Lie algebras and 4-invariants. Zbl 0998.57034
Soboleva, E.
2001
Thistlethwaite’s theorem for virtual links. Zbl 1163.57001
Chmutov, Sergei; Voltz, Jeremy
2008
On random knots. Zbl 0846.57003
Diao, Yuanan; Pippenger, Nicholas; Sumners, De Witt
1994
The genus of closed 3-braids. Zbl 0773.57007
Xu, Peijun
1992
Band surgery on knots and links. Zbl 1213.57011
Kanenobu, Taizo
2010
The knotting of equilateral polygons in $$\mathbb{R}^ 3$$. Zbl 0846.57004
Diao, Yuanan
1995
TQFT’s from homotopy 2-types. Zbl 0787.57002
Yetter, David N.
1993
Colored ribbon Hopf algebras and universal invariants of framed links. Zbl 0798.57006
1993
Lissajous knots. Zbl 0834.57005
Bogle, M. G. V.; Hearst, J. E.; Jones, V. F. R.; Stoilov, L.
1994
Geometric knot spaces and polygonal isotopy. Zbl 1001.57024
Calvo, Jorge Alberto
2001
Trace fields of twist knots. Zbl 1003.57014
Hoste, Jim; Shanahan, Patrick D.
2001
Links with trivial Jones polynomial. Zbl 1001.57022
Thistlethwaite, Morwen
2001
Intrinsically $$n$$-linked graphs. Zbl 0998.57008
Flapan, Erica; Pommersheim, James; Foisy, Joel; Naimi, Ramin
2001
A new point of view in the theory of knot and link invariants. Zbl 1002.57026
Labastida, José M. F.; Mariño, Marcos
2002
An oriented model for Khovanov homology. Zbl 1195.57024
Blanchet, Christian
2010
Markov trace on the Yokonuma-Hecke algebra. Zbl 1100.20008
Juyumaya, J.
2004
Markov theorem for transversal links. Zbl 1046.57007
Orevkov, S. Yu.; Shevchishin, V. V.
2003
Gauss’ linking number revisited. Zbl 1230.57009
Ricca, Renzo L.; Nipoti, Bernardo
2011
A table of genus two handlebody-knots up to six crossings. Zbl 1236.57015
Ishii, Atsushi; Kishimoto, Kengo; Moriuchi, Hiromasa; Suzuki, Masaaki
2012
Hopfological algebra and categorification at a root of unity: the first steps. Zbl 1370.18017
Khovanov, Mikhail
2016
Tangle decompositions of tunnel number one knots and links. Zbl 0841.57012
Gordon, C. McA.; Reid, A. W.
1995
On the orbit decomposition of finite quandles. Zbl 1105.57006
Nelson, Sam; Wong, Chau-Yim
2006
Quantum groups at roots of unity and modularity. Zbl 1117.17006
Sawin, Stephen F.
2006
A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum. Zbl 0818.57006
Kobayashi, Tsuyoshi
1994
Bicategories for TQFTs with defects with structure. Zbl 07516327
Lee, I. J.; Yetter, D. N.
2022
On linear resolvability of universal quantum dimensions. Zbl 07527799
Avetisyan, M. Y.; Mkrtchyan, R. L.
2022
The quantum trace as a quantum non-abelianization map. Zbl 07566140
Korinman, J.; Quesney, A.
2022
A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003
Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu
2021
Polynomial invariants of singular knots and links. Zbl 1464.57009
Ceniceros, Jose; Churchill, Indu R.; Elhamdadi, Mohamed
2021
Tied links in the solid torus. Zbl 1462.57004
Flores, Marcelo
2021
Arrow diagrams on spherical curves and computations. Zbl 1476.57009
Ito, Noboru; Takamura, Masashi
2021
The colored Jones polynomial and Kontsevich-Zagier series for double twist knots. Zbl 1470.57023
Lovejoy, Jeremy; Osburn, Robert
2021
More 1-cocycles for classical knots. Zbl 1470.57008
Fiedler, Thomas
2021
Superbridge and bridge indices for knots. Zbl 1466.57002
Adams, Colin; Agarwal, Nikhil; Allen, Rachel; Khandhawit, Tirasan; Simons, Alex; Winarski, Rebecca; Wootters, Mary
2021
Quandle coloring quivers of links using dihedral quandles. Zbl 1468.57007
Taniguchi, Yuta
2021
The reduced Dijkgraaf-Witten invariant of twist knots in the Bloch group of a finite field. Zbl 1478.57006
Karuo, Hiroaki
2021
Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions. Zbl 1467.57015
Oshiro, Kanako; Oyamaguchi, Natsumi
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 1467.57005
Lee, Sangyop
2021
Group presentations for links in thickened surfaces. Zbl 1472.57008
Silver, Daniel S.; Williams, Susan G.
2021
A relation between the crossing number and the height of a knotoid. Zbl 1479.57024
2021
A free-group valued invariant of free knots. Zbl 1473.57028
Manturov, Vassily Olegovich
2021
Writhe-like invariants of alternating links. Zbl 1464.57001
Diao, Yuanan; Pham, Van
2021
Tied links in various topological settings. Zbl 1487.57004
Diamantis, Ioannis
2021
Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces. Zbl 1484.57007
Kauffman, Louis H.; Nikonov, Igor Mikhailovich; Ogasa, Eiji
2021
Local-moves on knots and products of knots. II. Zbl 1485.57020
Kauffman, Louis H.; Ogasa, Eiji
2021
Symmetric union presentations for 2-bridge ribbon knots. Zbl 1486.57011
Lamm, Christoph
2021
Torsion in Khovanov homology of homologically thin knots. Zbl 1490.57012
Shumakovitch, Alexander N.
2021
BPS spectra and 3-manifold invariants. Zbl 1448.57020
Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun
2020
Large color $$R$$-matrix for knot complements and strange identities. Zbl 1460.57014
Park, Sunghyuk
2020
A lower bound of crosscap numbers of alternating knots. Zbl 1436.57006
Ito, Noboru; Takimura, Yusuke
2020
Planar pure braids on six strands. Zbl 07182541
Mostovoy, Jacob; Roque-Márquez, Christopher
2020
Multivariate Alexander quandles. I: The module sequence of a link. Zbl 1440.57011
Traldi, Lorenzo
2020
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves. Zbl 1458.57005
Gill, Amrendra; Prabhakar, Madeti; Vesnin, Andrei
2020
Picture-valued parity-biquandle bracket. Zbl 1439.57028
Ilyutko, Denis P.; Manturov, Vassily O.
2020
Functoriality of Khovanov homology. Zbl 1481.57020
Vogel, Pierre
2020
$$F$$-polynomials of tabulated virtual knots. Zbl 1447.57009
Ivanov, Maxim; Vesnin, Andrei
2020
Khovanov homology and diagonalizable Frobenius algebras. Zbl 1434.57011
Turner, Paul
2020
Erratum to: “Multivariate Alexander quandles. II. The involutory medial quandle of a link”. Zbl 1460.57007
Traldi, Lorenzo
2020
Refined Chern-Simons theory in genus two. Zbl 1450.57010
Arthamonov, S.; Shakirov, Sh.
2020
A note on coverings of virtual knots. Zbl 1478.57011
Nakamura, Takuji; Nakanishi, Yasutaka; Satoh, Shin
2020
Torsion calculations in Khovanov cohomology. Zbl 1462.57019
Schütz, Dirk
2020
Twisted torus knots $$T(p,q,p-kq,-1)$$ which are torus knots. Zbl 1452.57006
Lee, Sangyop
2020
A note on representations of welded braid groups. Zbl 07291658
Bellingeri, Paolo; Soulié, Arthur
2020
Multistring based matrices. Zbl 07240989
Freund, David R.
2020
Kauffman skein algebras and quantum Teichmüller spaces via factorization homology. Zbl 1471.57016
Cooke, Juliet
2020
A complete invariant for connected surfaces in the 3-sphere. Zbl 1439.57041
Bellettini, Giovanni; Paolini, Maurizio; Wang, Yi-Sheng
2020
An estimation for the ascending numbers of knots by $${\Gamma}$$-polynomials. Zbl 1435.57003
Higa, Ryuji
2020
3-manifolds with abelian embeddings in $$S^4$$. Zbl 1441.57022
Hillman, J. A.
2020
Labels instead of coefficients: a label bracket $$[\cdot]_{\mathcal{L}}$$ which dominates the Jones polynomial $$\mathcal{X}(\cdot)$$, the kuperberg bracket $$|\cdot\rangle_{a_2}$$, and the normalized arrow polynomial $$\mathcal{W}[\cdot]$$. Zbl 1441.57009
Akimova, Alyona A.; Manturov, Vassily O.
2020
From biquandle structures to Hom-biquandles. Zbl 1451.57002
Horvat, E.; Crans, A. S.
2020
Triple-crossing projections, moves on knots and links and their minimal diagrams. Zbl 1444.57003
Jabłonowski, Michał; Trojanowski, Łukasz
2020
Variational formulae and estimates of O’Hara’s knot energies. Zbl 1441.53001
Kawakami, Shoya; Nagasawa, Takeyuki
2020
Braid index bounds ropelength from below. Zbl 1439.57009
Diao, Yuanan
2020
The Tutte polynomial of symmetric hyperplane arrangements. Zbl 1439.52026
Randriamaro, Hery
2020
A neural network approach to predicting and computing knot invariants. Zbl 1439.57015
Hughes, Mark C.
2020
The knot Floer cube of resolutions and the composition product. Zbl 1476.57018
Dowlin, Nathan
2020
On Legendrian cobordisms and generating functions. Zbl 1441.53068
Limouzineau, Maÿlis
2020
Knots with exactly 10 sticks. Zbl 1439.57005
Blair, Ryan; Eddy, Thomas D.; Morrison, Nathaniel; Shonkwiler, Clayton
2020
Comparing nonorientable three genus and nonorientable four genus of torus knots. Zbl 1439.57016
Jabuka, Stanislav; Van Cott, Cornelia A.
2020
Knot-theoretic flocks. Zbl 1448.57009
Niebrzydowski, Maciej; Pilitowska, Agata; Zamojska-Dzienio, Anna
2020
State sum invariants for flat virtual links from the chord index. Zbl 1464.57011
Lee, Kyeonghui; Im, Young Ho; Kim, Sera
2020
Raising crosscap number while lowering unknotting number. Zbl 1443.57003
Kerian, A.
2020
On realizability of Gauss diagrams and constructions of meanders. (On realizabilty of Gauss diagrams and constructions of meanders.) Zbl 1473.57012
Grinblat, Andrey; Lopatkin, Viktor
2020
Mapping class group representations from Drinfeld doubles of finite groups. Zbl 1448.57018
2020
DNA origami and unknotted A-trails in torus graphs. Zbl 1447.05063
Morse, Ada; Adkisson, William; Greene, Jessica; Perry, David; Smith, Brenna; Ellis-Monaghan, Jo; Pangborn, Greta
2020
A multiple group rack and oriented spatial surfaces. Zbl 1447.57008
Ishii, Atsushi; Matsuzaki, Shosaku; Murao, Tomo
2020
Cuspidal edges with the same first fundamental forms along a knot. Zbl 1455.57032
Honda, Atsufumi; Naokawa, Kosuke; Saji, Kentaro; Umehara, Masaaki; Yamada, Kotaro
2020
Presentation of a ribbon $$2$$-knot. Zbl 1448.57022
Kanenobu, Taizo; Matsuda, Masafumi
2020
Crossing change on Khovanov homology and a categorified Vassiliev skein relation. Zbl 1476.57019
Ito, Noboru; Yoshida, Jun
2020
On Bennequin-type inequalities for links in tight contact 3-manifolds. Zbl 1450.57005
Cavallo, Alberto
2020
Positive knots and weak $$(1, 3)$$ homotopy. Zbl 1451.57003
Ito, Noboru; Takimura, Yusuke
2020
On 3-strand singular pure braid group. Zbl 07291634
Bardakov, Valeriy G.; Kozlovskaya, Tatyana A.
2020
Some remarks on the chord index. Zbl 1464.57010
Cheng, Zhiyun; Gao, Hongzhu; Xu, Mengjian
2020
Knotting probability of an arc diagram. Zbl 1460.57004
Kawauchi, Akio
2020
Some remarks on twin groups. Zbl 07291639
Naik, Tushar K.; Nanda, Neha; Singh, Mahender
2020
Black holes and topological surgery. Zbl 1455.57023
Antoniou, Stathis; Kauffman, Louis H.; Lambropoulou, Sofia
2020
Chbili, Nafaa; Kaur, Kirandeep
2020
Minimal grid diagrams of 11 crossing prime alternating knots. Zbl 1456.57005
Jin, Gyo Taek; Lee, Hwa Jeong
2020
Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher-Thurston graphs. Zbl 1459.57019
Irmak, Elmas
2020
On fertility of knot shadows. Zbl 1455.57011
Hanaki, Ryo
2020
Interior polynomial for signed bipartite graphs and the HOMFLY polynomial. Zbl 1464.57015
Kato, Keiju
2020
Genera of knots in the complex projective plane. Zbl 1464.57006
Pichelmeyer, Jake
2020
Shake slice and shake concordant links. Zbl 1469.57002
Bosman, Anthony M.
2020
String-net models for nonspherical pivotal fusion categories. Zbl 1445.18013
Runkel, Ingo
2020
A description of Rasmussen’s invariant from the divisibility of Lee’s canonical class. Zbl 07240988
Sano, Taketo
2020
The structure of biquandle brackets. Zbl 1448.57014
Hoffer, Will; Vengal, Adu; Winstein, Vilas
2020
The disk complex and topologically minimal surfaces in the 3-sphere. Zbl 1460.57018
Campisi, Marion; Torres, Luis
2020
Multivariate Alexander quandles. II: The involutory medial quandle of a link (corrected). Zbl 1460.57008
Traldi, Lorenzo
2020
3-manifolds with nilpotent embeddings in $$S^4$$. Zbl 1461.57007
Hillman, J. A.
2020
Unknotting numbers and crossing numbers of spatial embeddings of a planar graph. Zbl 1459.57003
Akimoto, Yuta; Taniyama, Kouki
2020
New computations of the superbridge index. Zbl 1460.57006
Shonkwiler, Clayton
2020
On the basic properties of $$G C_n$$ sets. Zbl 1457.41002
Hakopian, Hakop A.; Vardanyan, Navasard K.
2020
Biquandle coloring invariants of knotoids. Zbl 1428.57004
Gügümcü, Neslihan; Nelson, Sam
2019
An important step for the computation of the HOMFLYPT skein module of the Lens spaces $$L(p, 1)$$ via braids. Zbl 1452.57005
Diamantis, Ioannis; Lambropoulou, Sofia
2019
Constructing a polynomial whose nodal set is any prescribed knot or link. Zbl 1411.57010
Bode, Benjamin; Dennis, Mark R.
2019
Quandle coloring quivers. Zbl 1420.57032
Cho, Karina; Nelson, Sam
2019
Rail knotoids. Zbl 1436.57008
Kodokostas, Dimitrios; Lambropoulou, Sofia
2019
The Kauffman bracket skein module of the handlebody of genus 2 via braids. Zbl 07177783
Diamantis, Ioannis
2019
A bridge between Conway-Coxeter friezes and rational tangles through the Kauffman bracket polynomials. Zbl 1436.57009
Kogiso, Takeyoshi; Wakui, Michihisa
2019
Multivariate Alexander quandles. III. Sublinks. Zbl 1436.57011
Traldi, Lorenzo
2019
Graph polynomials and link invariants as positive type functions on Thompson’s group $$F$$. Zbl 1412.43007
Aiello, Valeriano; Conti, Roberto
2019
Virtual tribrackets. Zbl 1426.57029
Nelson, Sam; Pico, Shane
2019
Artin’s braids, braids for three space, and groups $${\Gamma}_n^4$$ and $$G_n^k$$. Zbl 1431.57005
Kim, Seongjeong; Manturov, V. O.
2019
Finite-type invariants of order one of long and framed virtual knots. Zbl 1447.57010
Petit, Nicolas
2019
...and 1231 more Documents
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### Cited by 3,583 Authors

 89 Kauffman, Louis Hirsch 60 Nelson, Sam 56 Manturov, Vassiliĭ Olegovich 48 Kamada, Seiichi 40 Stoimenow, Alexander 39 Saito, Masahico 36 Przytycki, Józef Henryk 34 Elhamdadi, Mohamed 32 Garoufalidis, Stavros 31 Bardakov, Valeriĭ Georgievich 31 Diao, Yuanan 30 Kawauchi, Akio 29 Jin, Xian’an 29 Lee, Sang Youl 29 Morozov, Alexei Yurievich 28 Carter, J. Scott 28 Oh, Seungsang 28 Satoh, Shin 27 Ito, Tetsuya 27 Kanenobu, Taizo 27 Lambropoulou, Sofia S. F. 26 Silver, Daniel S. 25 Adams, Colin C. 25 Ishii, Atsushi 25 Ito, Noboru 24 Kamada, Naoko 24 Tran, Anh Tuan 24 Williams, Susan G. 23 East, James 23 Mironov, Andrei D. 23 Oshiro, Kanako 22 Im, Young Ho 22 Le, Thang Tu Quoc 22 Ozawa, Makoto 22 Patureau-Mirand, Bertrand 22 Yasuhara, Akira 21 Ernst, Claus 21 Geer, Nathan 21 Ichihara, Kazuhiro 21 Mellor, Blake 21 Nakanishi, Yasutaka 21 Orevkov, Stepan Yur’evich 21 Spaggiari, Fulvia 20 Cavicchioli, Alberto 20 Traldi, Lorenzo 18 Andersen, Jørgen Ellegaard 18 Bellingeri, Paolo 18 Chbili, Nafaa 18 Guaschi, John 18 Jablan, Slavik Vlado 18 Jeong, Myeong-Ju 18 Mattman, Thomas W. 18 Vesnin, Andrei Yu. 17 Bae, Yongju 17 Cheng, Zhiyun 17 Frohman, Charles D. 17 Khovanov, Mikhail G. 17 Nikkuni, Ryo 17 Ohyama, Yoshiyuki 17 Shimizu, Ayaka 17 Xue, Kang 16 Dehornoy, Patrick 16 Lei, Fengchun 16 Meilhan, Jean-Baptiste 15 Dye, Heather Ann 15 Gonçalves, Daciberg Lima 15 Jin, Gyo Taek 15 Kalfagianni, Efstratia 15 Lee, Hwa Jeong 15 Lopes, Pedro 15 Motegi, Kimihiko 15 Nakamura, Takuji 14 Boden, Hans U. 14 Cristofori, Paola 14 Eudave-Muñoz, Mario 14 Fleming, Thomas R. 14 Gukov, Sergei 14 Hoste, Jim 14 Kim, Sera 14 Lauda, Aaron D. 14 Livingston, Charles 14 Martin, Paul Purdon 14 Nosaka, Takefumi 14 Ramadevi, Pichai 14 Rowell, Eric C. 14 Sazdanović, Radmila 14 Shima, Akiko 14 Takimura, Yusuke 14 Taniyama, Kouki 14 Teragaito, Masakazu 14 Wang, Zhenghan 13 Baker, Kenneth L. 13 Chrisman, Micah Whitney 13 Gilmer, Patrick M. 13 Hedden, Matthew 13 Kadokami, Teruhisa 13 Kofman, Ilya 13 Lebed, Victoria 13 Moffatt, Iain 13 Murakami, Jun ...and 3,483 more Authors
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### Cited in 391 Journals

 1,446 Journal of Knot Theory and its Ramifications 410 Topology and its Applications 280 Algebraic & Geometric Topology 116 Journal of Algebra 114 Transactions of the American Mathematical Society 111 Proceedings of the American Mathematical Society 105 Advances in Mathematics 87 Communications in Mathematical Physics 80 Journal of Pure and Applied Algebra 71 Geometry & Topology 65 Osaka Journal of Mathematics 62 Journal of High Energy Physics 61 Quantum Topology 55 International Journal of Mathematics 53 Geometriae Dedicata 50 Journal of Mathematical Physics 50 Mathematical Proceedings of the Cambridge Philosophical Society 44 Communications in Algebra 39 Mathematische Zeitschrift 34 European Journal of Combinatorics 33 Journal of Geometry and Physics 32 Nuclear Physics. B 32 Journal of Mathematical Sciences (New York) 31 Journal of the Mathematical Society of Japan 31 Experimental Mathematics 30 Letters in Mathematical Physics 30 Mathematische Annalen 30 Tokyo Journal of Mathematics 26 Journal of Algebraic Combinatorics 24 Discrete Mathematics 23 International Journal of Algebra and Computation 22 Journal of Combinatorial Theory. Series A 21 Inventiones Mathematicae 21 Quantum Information Processing 20 Selecta Mathematica. New Series 20 Journal of Algebra and its Applications 18 Duke Mathematical Journal 18 Advances in Applied Mathematics 17 Chaos, Solitons and Fractals 17 Fundamenta Mathematicae 17 The Electronic Journal of Combinatorics 16 Acta Mathematica Vietnamica 16 Annales de l’Institut Fourier 15 Boletín de la Sociedad Matemática Mexicana. Third Series 15 Algebras and Representation Theory 15 Communications in Contemporary Mathematics 14 International Journal of Modern Physics A 14 Discrete & Computational Geometry 14 Forum Mathematicum 14 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 14 Mediterranean Journal of Mathematics 14 Proceedings of the Steklov Institute of Mathematics 14 Journal of Topology 13 Bulletin of the Australian Mathematical Society 13 Israel Journal of Mathematics 13 Michigan Mathematical Journal 13 The New York Journal of Mathematics 13 Journal of the Australian Mathematical Society 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 13 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 12 Manuscripta Mathematica 12 Siberian Mathematical Journal 12 Bulletin of the American Mathematical Society. New Series 12 Annales Henri Poincaré 11 Compositio Mathematica 11 Pacific Journal of Mathematics 11 Acta Mathematica Sinica. English Series 11 Journal of Physics A: Mathematical and Theoretical 11 Journal of Topology and Analysis 10 Theoretical and Mathematical Physics 10 Journal für die Reine und Angewandte Mathematik 9 Discrete Applied Mathematics 9 Glasgow Mathematical Journal 9 Kyungpook Mathematical Journal 9 Proceedings of the Edinburgh Mathematical Society. Series II 9 Journal of Symbolic Computation 9 Sibirskie Èlektronnye Matematicheskie Izvestiya 9 Winter Braids Lecture Notes 8 Journal of Statistical Physics 8 Mathematical Notes 8 Reviews in Mathematical Physics 8 Indiana University Mathematics Journal 8 Journal of Combinatorial Theory. Series B 8 Semigroup Forum 8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 8 Journal of Mathematical Chemistry 8 Doklady Mathematics 8 Groups, Geometry, and Dynamics 8 Research in the Mathematical Sciences 7 International Journal of Theoretical Physics 7 Applied Mathematics and Computation 7 Canadian Mathematical Bulletin 7 Functional Analysis and its Applications 7 Journal of Graph Theory 7 Journal of the London Mathematical Society. Second Series 7 Graphs and Combinatorics 7 Linear Algebra and its Applications 7 Applied Categorical Structures 7 Transformation Groups ...and 291 more Journals
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### Cited in 58 Fields

 4,084 Manifolds and cell complexes (57-XX) 886 Group theory and generalizations (20-XX) 495 Quantum theory (81-XX) 493 Combinatorics (05-XX) 336 Associative rings and algebras (16-XX) 268 Nonassociative rings and algebras (17-XX) 250 Category theory; homological algebra (18-XX) 226 Differential geometry (53-XX) 199 Algebraic geometry (14-XX) 191 Algebraic topology (55-XX) 149 Global analysis, analysis on manifolds (58-XX) 108 Dynamical systems and ergodic theory (37-XX) 96 Number theory (11-XX) 91 Computer science (68-XX) 74 Several complex variables and analytic spaces (32-XX) 74 Relativity and gravitational theory (83-XX) 73 Functional analysis (46-XX) 68 Statistical mechanics, structure of matter (82-XX) 68 Biology and other natural sciences (92-XX) 57 Order, lattices, ordered algebraic structures (06-XX) 44 Probability theory and stochastic processes (60-XX) 39 Topological groups, Lie groups (22-XX) 38 Convex and discrete geometry (52-XX) 37 Functions of a complex variable (30-XX) 35 Geometry (51-XX) 33 Commutative algebra (13-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 30 General algebraic systems (08-XX) 29 Linear and multilinear algebra; matrix theory (15-XX) 29 Special functions (33-XX) 22 Numerical analysis (65-XX) 21 Mathematical logic and foundations (03-XX) 21 Partial differential equations (35-XX) 20 General topology (54-XX) 16 $$K$$-theory (19-XX) 14 Fluid mechanics (76-XX) 14 Information and communication theory, circuits (94-XX) 13 History and biography (01-XX) 13 Optics, electromagnetic theory (78-XX) 12 Field theory and polynomials (12-XX) 12 Statistics (62-XX) 12 Mechanics of deformable solids (74-XX) 11 General and overarching topics; collections (00-XX) 10 Real functions (26-XX) 10 Measure and integration (28-XX) 10 Mechanics of particles and systems (70-XX) 8 Ordinary differential equations (34-XX) 8 Approximations and expansions (41-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Systems theory; control (93-XX) 5 Difference and functional equations (39-XX) 3 Abstract harmonic analysis (43-XX) 3 Operator theory (47-XX) 3 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Mathematics education (97-XX)