Edit Profile (opens in new tab) Manturov, Vassiliĭ Olegovich Co-Author Distance Author ID: manturov.vassily-olegovich Published as: Manturov, V. O.; Manturov, Vassily Olegovich; Manturov, Vassily O.; Manturov, Vassily; Manturov, Vassiliĭ O. more...less Further Spellings: Мантуров Василий Олегович Homepage: http://fn.bmstu.ru/research-section-sec-fs/personalities-fs/item/529-manturov-v-... External Links: MGP · ResearchGate · Math-Net.Ru · GND Documents Indexed: 147 Publications since 2000, including 4 Books and 31 Additional arXiv Preprints 8 Contributions as Editor Reviewing Activity: 33 Reviews Co-Authors: 42 Co-Authors with 80 Joint Publications 1,008 Co-Co-Authors all top 5 Co-Authors 75 single-authored 18 Nikonov, Igor Mikhailovich 16 Il’yutko, Denis Petrovich 12 Kauffman, Louis Hirsch 11 Fedoseev, Denis Aleksandrovich 11 Kim, Seongjeong 3 Cheng, Zhiyun 3 Chrisman, Micah Whitney 3 Lee, Sang Youl 3 Wan, Zheyan 2 Afanasiev, Denis Mikhailovich 2 Akimova, Alena Andreevna 2 Bae, Yongju 2 Campoamor-Stursberg, Rutwig 2 Fenn, Roger A. 2 Friesen, Tyler 2 Manturov, Oleg V. 1 Akbulut, Selman 1 Bardakov, Valeriĭ Georgievich 1 Bauer, Stefan Alois 1 Carter, J. Scott 1 Chu, Karene 1 Dye, Heather Ann 1 Gaifullin, Alexander A. 1 Gao, Hongzhu 1 Kamada, Seiichi 1 Kanel’-Belov, Alekseĭ Yakovlevich 1 Karpov, A. B. 1 Kawauchi, Akio 1 Kim, Sera 1 King, Simon A. 1 Krasnov, Vladimir Aleksandrovich 1 Krylov, D. Yu. 1 Matveev, Sergeĭ Vladimirovich 1 Moshchevitin, Nikolay G. 1 Orr, Kent E. 1 Przytycki, Józef Henryk 1 Rushworth, William 1 Schneiderman, Rob 1 Vesnin, Andrei Yu. 1 Wang, Hang 1 Wu, Jie 1 Xu, Mengjian 1 Yang, Zhiqing 1 Zenkina, M. V. all top 5 Serials 49 Journal of Knot Theory and its Ramifications 16 Doklady Mathematics 11 Journal of Mathematical Sciences (New York) 3 Moscow University Mathematics Bulletin 3 Russian Mathematical Surveys 3 Fundamenta Mathematicae 3 Transactions of the Moscow Mathematical Society 3 Acta Applicandae Mathematicae 3 Sbornik: Mathematics 3 Oberwolfach Reports 3 Series on Knots and Everything 2 Izvestiya: Mathematics 1 Mathematical Notes 1 Monatshefte für Mathematik 1 European Journal of Combinatorics 1 Fundamental’naya i Prikladnaya Matematika 1 Reviews in Mathematics and Mathematical Physics 1 Lobachevskii Journal of Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Quantum Topology 1 Bulletin of Mathematical Sciences all top 5 Fields 142 Manifolds and cell complexes (57-XX) 21 Group theory and generalizations (20-XX) 15 Combinatorics (05-XX) 8 General and overarching topics; collections (00-XX) 4 Commutative algebra (13-XX) 4 Nonassociative rings and algebras (17-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Differential geometry (53-XX) 3 Algebraic geometry (14-XX) 3 Algebraic topology (55-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 98 Publications have been cited 748 times in 347 Documents Cited by ▼ Year ▼ Parity in knot theory. Zbl 1210.57010 Manturov, V. O. 74 2010 Virtual knots. The state of the art. Zbl 1270.57003 Manturov, Vassily Olegovich; Ilyutko, Denis Petrovich 54 2013 Virtual knot theory – unsolved problems. Zbl 1084.57005 Fenn, Roger; Kauffman, Louis H.; Manturov, Vassily O. 32 2005 Knot theory. Zbl 1052.57001 Manturov, Vassily 31 2004 Virtual biquandles. Zbl 1088.57006 Kauffman, Louis H.; Manturov, Vassily O. 29 2005 Parity in knot theory and graph-links. Zbl 1320.57001 Ilyutko, D. P.; Manturov, V. O.; Nikonov, I. M. 24 2013 On invariants of virtual links. Zbl 1003.57005 Manturov, V. O. 22 2002 Parity and projection from virtual knots to classical knots. Zbl 1280.57007 Manturov, Vassily Olegovich 22 2013 Khovanov homology for virtual knots with arbitrary coefficients. Zbl 1117.57013 Manturov, Vassily Olegovich 20 2007 Free knots and groups. Zbl 1195.57018 Manturov, O. V.; Manturov, V. O. 19 2010 Long virtual knots and their invariants. Zbl 1064.57005 Manturov, Vassily O. 18 2004 Virtual knots and links. Zbl 1351.57012 Kauffman, L. H.; Manturov, V. O. 17 2006 Kauffman-like polynomial and curves in 2-surfaces. Zbl 1059.57006 Manturov, Vassily O. 14 2003 Parity and cobordism of free knots. Zbl 1259.05047 Manturov, V. O. 13 2012 Khovanov homology for virtual knots with arbitrary coefficients. Zbl 1142.57007 Manturov, V. O. 13 2007 Parity and patterns in low dimensional topology. Zbl 1387.57025 Ilyutko, D. P.; Manturov, V. O.; Nikonov, I. M. 12 2015 A proof of Vassiliev’s conjecture on the planarity of singular links. Zbl 1122.05030 Manturov, V. O. 12 2005 Virtual knot invariants arising from parities. Zbl 1322.57006 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 11 2014 Introduction to graph-link theory. Zbl 1189.57006 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich 11 2009 Bifurcations, atoms and knots. Zbl 0979.37028 Manturov, V. O. 10 2000 Multi-variable polynomial invariants for virtual links. Zbl 1061.57013 Manturov, Vassily O. 10 2003 On two categorifications of the arrow polynomial for virtual knots. Zbl 1221.57016 Dye, Heather Ann; Kauffman, Louis Hirsch; Manturov, Vassily Olegovich 10 2011 Unsolved problems in virtual knot theory and combinatorial knot theory. Zbl 1310.57010 Fenn, Roger; Ilyutko, Denis P.; Kauffman, Louis H.; Manturov, Vassily O. 9 2014 Free knots and parity. Zbl 1273.57008 Manturov, V. O. 9 2012 Atoms and minimal diagrams of virtual links. Zbl 1125.57300 Manturov, V. O. 9 2003 On braids and groups \(G_n^k\). Zbl 1339.20033 Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 8 2015 The groups \(G_n^k\) and fundamental groups of configuration spaces. Zbl 1367.57005 Manturov, V. O. 8 2017 The groups \(G_n^2\) and Coxeter groups. Zbl 1371.20039 Manturov, V. O. 8 2017 Vassiliev invariants for virtual links, curves on surfaces and the Jones-Kauffman polynomial. Zbl 1071.57011 Manturov, Vassily O. 8 2005 On virtual crossing number estimates for virtual links. Zbl 1183.57002 Afanasiev, Denis Mikhailovich; Manturov, Vassily Olegovich 7 2009 A graphical construction of the sl(3) invariant for virtual knots. Zbl 1326.57018 Kauffman, Louis H.; Manturov, Vassily O. 7 2014 A combinatorial representation of links by quasitoric braids. Zbl 0991.57007 Manturov, V. O. 6 2002 Fibered knots and virtual knots. Zbl 1325.57003 Chrisman, Micah W.; Manturov, Vassily O. 6 2013 An almost classification of free knots. Zbl 1284.57011 Manturov, V. O. 6 2013 Parity, free knots, groups, and invariants of finite type. Zbl 1246.57019 Manturov, V. O. 6 2011 The Khovanov complex and minimal knot diagrams. Zbl 1155.57303 Manturov, V. O. 6 2006 Graph-links. Zbl 1180.57012 Il’yutko, D. P.; Manturov, V. O. 6 2009 Picture-valued parity-biquandle bracket. Zbl 1439.57028 Ilyutko, Denis P.; Manturov, Vassily O. 6 2020 Cobordisms of free knots. Zbl 1196.57005 Il’yutko, D. P.; Manturov, V. O. 6 2009 Invariants and pictures. Low-dimensional topology and combinatorial group theory. Zbl 1447.57001 Manturov, Vassily Olegovich; Fedoseev, Denis; Kim, Seongjeong; Nikonov, Igor 6 2020 Recognition of virtual braids. Zbl 1144.20310 Manturov, V. O. 6 2005 The Khovanov complex for virtual links. Zbl 1165.57012 Manturov, V. O. 6 2007 Invariant tensor formulas via chord diagrams. Zbl 1146.57016 Campoamor-Stursberg, R.; Manturov, V. O. 6 2005 Artin’s braids, braids for three space, and groups \({\Gamma}_n^4\) and \(G_n^k\). Zbl 1431.57005 Kim, Seongjeong; Manturov, V. O. 5 2019 Embeddings of 4-valent framed graphs into 2-surfaces. Zbl 1309.05054 Manturov, V. O. 5 2009 Graph-links. Zbl 1256.57007 Ilyutko, D. P.; Manturov, V. O. 5 2012 On polynomial invariants of virtual links. Zbl 1169.57302 Manturov, V. O. 5 2004 One-term parity bracket for braids. Zbl 1325.05158 Manturov, Vassily Olegovich 4 2015 Homotopical Khovanov homology. Zbl 1331.57018 Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 4 2015 Graphical constructions for the sl(3), \(C_2\) and \(G_2\) invariants for virtual knots, virtual braids and free knots. Zbl 1321.57010 Kauffman, Louis Hirsch; Manturov, Vassily Olegovich 4 2015 Invariants of virtual links. Zbl 1197.57014 Manturov, V. O. 4 2002 Graph-valued invariants of virtual and classical links and minimality problem. Zbl 1317.57003 Krasnov, Vladimir Aleksandrovich; Manturov, Vassily Olegovich 4 2013 Parity and exotic combinatorial formulae for finite-type invariants of virtual knots. Zbl 1275.57007 Chrisman, Micah Whitney; Manturov, Vassily Olegovich 4 2012 Markov theorem for free links. Zbl 1275.57014 Manturov, Vassily Olegovich; Wang, Hang 4 2012 On long virtual knots. Zbl 1272.57005 Manturov, V. O. 4 2005 Additional gradings in Khovanov homology. Zbl 1233.57007 Manturov, Vassily Olegovich 4 2008 Free knots and groups. Zbl 1261.57006 Manturov, V. O.; Manturov, O. V. 4 2010 Compact and long virtual knots. Zbl 1206.57008 Manturov, V. O. 4 2008 An invariant of links in a thickened torus. Zbl 1280.57011 Zenkina, M. V.; Manturov, V. O. 3 2011 Parities on 2-knots and 2-links. Zbl 1358.57026 Fedoseev, Denis A.; Manturov, Vassily O. 3 2016 Curves on surfaces virtual knots, and the Jones-Kaufmann polynomial. Zbl 1247.57011 Manturov, Vassily Olegovich 3 2003 On marked braid groups. Zbl 1337.57015 Fedoseev, Denis A.; Manturov, Vassily O.; Cheng, Zhiyun 2 2015 A parity map of framed chord diagrams. Zbl 1337.57003 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich 2 2015 Chord diagrams and invariant tensors. Zbl 1014.57010 Manturov, Vassily O. 2 2002 Maximally symmetric atoms and \(2 \times 2\) matrix groups. Zbl 1025.37015 Manturov, V. O. 2 2001 Knots and the bracket calculus. Zbl 1014.57003 Manturov, V. O. 2 2002 The bracket semigroup of knots. Zbl 0958.57010 Manturov, V. O. 2 2000 \(G_n^k\)-groups for simplicial complexes and the word problem on \(G^2(K)\). Zbl 1435.20045 Manturov, Vassily O.; Wu, J. 2 2018 Virtual knots and infinite-dimensional Lie algebras. Zbl 1065.57005 Manturov, Vassily O. 2 2004 Embeddings of \(\ast\)-graphs into 2-surfaces. Zbl 1278.05083 Friesen, Tyler; Manturov, Vassily Olegovich 2 2013 Flat hierarchy. Zbl 1088.57009 Manturov, Vassily O. 2 2005 On groups \(G_n^k\) and \(\Gamma_n^k\): a study of manifolds, dynamics, and invariants. Zbl 1489.57004 Manturov, Vassily O.; Fedoseev, Denis A.; Kim, Seongjeong; Nikonov, Igor M. 2 2021 From chord parity to chord index. Zbl 1459.57016 Cheng, Zhiyun; Fedoseev, Denis A.; Gao, Hongzhu; Manturov, Vassily O.; Xu, Mengjian 2 2020 On the chromatic numbers of integer and rational lattices. Zbl 1343.05065 Manturov, V. O. 2 2016 Additional gradings in the Khovanov complex for thickened surfaces. Zbl 1151.57303 Manturov, V. O. 2 2008 On the recognition of braids. Zbl 1040.57009 Gaifullin, Alexander A.; Manturov, Vassily O. 2 2002 Knot theory. 2nd edition. Zbl 1392.57001 Manturov, Vassily Olegovich 1 2018 An elementary proof that classical braids embed in virtual braids. Zbl 1353.57020 Manturov, V. O. 1 2016 New parities and coverings over free knots. Zbl 1368.57006 Manturov, Vassily Olegovich 1 2016 New ideas in low dimensional topology. Zbl 1314.57001 1 2015 Reidemeister moves and groups. Zbl 1325.05157 Manturov, Vassily Olegovich 1 2015 The group \(G_n^2\) and invariants of free links valued in free groups. Zbl 1353.57012 Manturov, V. O.; Kim, Seongjeong 1 2015 Additional gradings on generalizations of Khovanov homology and invariants of embedded surfaces. Zbl 1400.57009 Manturov, Vassily Olegovich; Rushworth, William 1 2018 Cobordisms of graphs: a sliceness criterion for stably odd free knots and related results on cobordisms. Zbl 1405.57037 Fedoseev, Denis A.; Manturov, Vassily O. 1 2018 Framed 4-valent graph minor theory. I: Introduction. A planarity criterion and linkless embeddability. Zbl 1302.05176 Manturov, Vassily Olegovich 1 2014 Checkerboard embeddings of \(\ast\)-graphs into nonorientable surfaces. Zbl 1305.05051 Friesen, Tyler; Manturov, Vassily Olegovich 1 2014 On groups \(G_n^k\), braids and Brunnian braids. Zbl 1359.57006 Kim, Seongjeong; Manturov, V. O. 1 2016 An invariant polynomial of two variables for virtual links. Zbl 1044.57003 Manturov, V. O. 1 2002 Virtual crossing numbers for virtual knots. Zbl 1275.57013 Manturov, Vassily Olegovich 1 2012 On minimal virtual link diagrams. Zbl 1176.57005 Afanasiev, D. M.; Manturov, V. O. 1 2009 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. 1 2020 Invariants of classical braids valued in \(G_n^2 \). Zbl 1511.20131 Manturov, V. O. 1 2021 A free-group valued invariant of free knots. Zbl 1473.57028 Manturov, Vassily Olegovich 1 2021 On long knots in the full torus. Zbl 1487.57008 Kim, Sera; Kim, Seongjeong; Manturov, Vassily O. 1 2022 Embeddings of four-valent framed graphs into 2-surfaces. Zbl 1219.05047 Manturov, Vassily Olegovich 1 2011 A sliceness criterion for odd free knots. Zbl 1444.57009 Manturov, Vassiliĭ O.; Fedoseev, Denis A. 1 2019 Finite-type invariants of virtual links and the Jones-Kauffman polynomial. Zbl 1282.57018 Manturov, V. O. 1 2004 Manifolds of triangulations, braid groups of manifolds, and the groups \(\Gamma_n^k\). Zbl 1489.57018 Fedoseev, Denis A.; Manturov, Vassily O.; Nikonov, Igor M. 1 2021 On long knots in the full torus. Zbl 1487.57008 Kim, Sera; Kim, Seongjeong; Manturov, Vassily O. 1 2022 On groups \(G_n^k\) and \(\Gamma_n^k\): a study of manifolds, dynamics, and invariants. Zbl 1489.57004 Manturov, Vassily O.; Fedoseev, Denis A.; Kim, Seongjeong; Nikonov, Igor M. 2 2021 Invariants of classical braids valued in \(G_n^2 \). Zbl 1511.20131 Manturov, V. O. 1 2021 A free-group valued invariant of free knots. Zbl 1473.57028 Manturov, Vassily Olegovich 1 2021 Manifolds of triangulations, braid groups of manifolds, and the groups \(\Gamma_n^k\). Zbl 1489.57018 Fedoseev, Denis A.; Manturov, Vassily O.; Nikonov, Igor M. 1 2021 Picture-valued parity-biquandle bracket. Zbl 1439.57028 Ilyutko, Denis P.; Manturov, Vassily O. 6 2020 Invariants and pictures. Low-dimensional topology and combinatorial group theory. Zbl 1447.57001 Manturov, Vassily Olegovich; Fedoseev, Denis; Kim, Seongjeong; Nikonov, Igor 6 2020 From chord parity to chord index. Zbl 1459.57016 Cheng, Zhiyun; Fedoseev, Denis A.; Gao, Hongzhu; Manturov, Vassily O.; Xu, Mengjian 2 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. 1 2020 Artin’s braids, braids for three space, and groups \({\Gamma}_n^4\) and \(G_n^k\). Zbl 1431.57005 Kim, Seongjeong; Manturov, V. O. 5 2019 A sliceness criterion for odd free knots. Zbl 1444.57009 Manturov, Vassiliĭ O.; Fedoseev, Denis A. 1 2019 \(G_n^k\)-groups for simplicial complexes and the word problem on \(G^2(K)\). Zbl 1435.20045 Manturov, Vassily O.; Wu, J. 2 2018 Knot theory. 2nd edition. Zbl 1392.57001 Manturov, Vassily Olegovich 1 2018 Additional gradings on generalizations of Khovanov homology and invariants of embedded surfaces. Zbl 1400.57009 Manturov, Vassily Olegovich; Rushworth, William 1 2018 Cobordisms of graphs: a sliceness criterion for stably odd free knots and related results on cobordisms. Zbl 1405.57037 Fedoseev, Denis A.; Manturov, Vassily O. 1 2018 The groups \(G_n^k\) and fundamental groups of configuration spaces. Zbl 1367.57005 Manturov, V. O. 8 2017 The groups \(G_n^2\) and Coxeter groups. Zbl 1371.20039 Manturov, V. O. 8 2017 Parities on 2-knots and 2-links. Zbl 1358.57026 Fedoseev, Denis A.; Manturov, Vassily O. 3 2016 On the chromatic numbers of integer and rational lattices. Zbl 1343.05065 Manturov, V. O. 2 2016 An elementary proof that classical braids embed in virtual braids. Zbl 1353.57020 Manturov, V. O. 1 2016 New parities and coverings over free knots. Zbl 1368.57006 Manturov, Vassily Olegovich 1 2016 On groups \(G_n^k\), braids and Brunnian braids. Zbl 1359.57006 Kim, Seongjeong; Manturov, V. O. 1 2016 Parity and patterns in low dimensional topology. Zbl 1387.57025 Ilyutko, D. P.; Manturov, V. O.; Nikonov, I. M. 12 2015 On braids and groups \(G_n^k\). Zbl 1339.20033 Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 8 2015 One-term parity bracket for braids. Zbl 1325.05158 Manturov, Vassily Olegovich 4 2015 Homotopical Khovanov homology. Zbl 1331.57018 Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 4 2015 Graphical constructions for the sl(3), \(C_2\) and \(G_2\) invariants for virtual knots, virtual braids and free knots. Zbl 1321.57010 Kauffman, Louis Hirsch; Manturov, Vassily Olegovich 4 2015 On marked braid groups. Zbl 1337.57015 Fedoseev, Denis A.; Manturov, Vassily O.; Cheng, Zhiyun 2 2015 A parity map of framed chord diagrams. Zbl 1337.57003 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich 2 2015 New ideas in low dimensional topology. Zbl 1314.57001 1 2015 Reidemeister moves and groups. Zbl 1325.05157 Manturov, Vassily Olegovich 1 2015 The group \(G_n^2\) and invariants of free links valued in free groups. Zbl 1353.57012 Manturov, V. O.; Kim, Seongjeong 1 2015 Virtual knot invariants arising from parities. Zbl 1322.57006 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich; Nikonov, Igor Mikhailovich 11 2014 Unsolved problems in virtual knot theory and combinatorial knot theory. Zbl 1310.57010 Fenn, Roger; Ilyutko, Denis P.; Kauffman, Louis H.; Manturov, Vassily O. 9 2014 A graphical construction of the sl(3) invariant for virtual knots. Zbl 1326.57018 Kauffman, Louis H.; Manturov, Vassily O. 7 2014 Framed 4-valent graph minor theory. I: Introduction. A planarity criterion and linkless embeddability. Zbl 1302.05176 Manturov, Vassily Olegovich 1 2014 Checkerboard embeddings of \(\ast\)-graphs into nonorientable surfaces. Zbl 1305.05051 Friesen, Tyler; Manturov, Vassily Olegovich 1 2014 Virtual knots. The state of the art. Zbl 1270.57003 Manturov, Vassily Olegovich; Ilyutko, Denis Petrovich 54 2013 Parity in knot theory and graph-links. Zbl 1320.57001 Ilyutko, D. P.; Manturov, V. O.; Nikonov, I. M. 24 2013 Parity and projection from virtual knots to classical knots. Zbl 1280.57007 Manturov, Vassily Olegovich 22 2013 Fibered knots and virtual knots. Zbl 1325.57003 Chrisman, Micah W.; Manturov, Vassily O. 6 2013 An almost classification of free knots. Zbl 1284.57011 Manturov, V. O. 6 2013 Graph-valued invariants of virtual and classical links and minimality problem. Zbl 1317.57003 Krasnov, Vladimir Aleksandrovich; Manturov, Vassily Olegovich 4 2013 Embeddings of \(\ast\)-graphs into 2-surfaces. Zbl 1278.05083 Friesen, Tyler; Manturov, Vassily Olegovich 2 2013 Parity and cobordism of free knots. Zbl 1259.05047 Manturov, V. O. 13 2012 Free knots and parity. Zbl 1273.57008 Manturov, V. O. 9 2012 Graph-links. Zbl 1256.57007 Ilyutko, D. P.; Manturov, V. O. 5 2012 Parity and exotic combinatorial formulae for finite-type invariants of virtual knots. Zbl 1275.57007 Chrisman, Micah Whitney; Manturov, Vassily Olegovich 4 2012 Markov theorem for free links. Zbl 1275.57014 Manturov, Vassily Olegovich; Wang, Hang 4 2012 Virtual crossing numbers for virtual knots. Zbl 1275.57013 Manturov, Vassily Olegovich 1 2012 On two categorifications of the arrow polynomial for virtual knots. Zbl 1221.57016 Dye, Heather Ann; Kauffman, Louis Hirsch; Manturov, Vassily Olegovich 10 2011 Parity, free knots, groups, and invariants of finite type. Zbl 1246.57019 Manturov, V. O. 6 2011 An invariant of links in a thickened torus. Zbl 1280.57011 Zenkina, M. V.; Manturov, V. O. 3 2011 Embeddings of four-valent framed graphs into 2-surfaces. Zbl 1219.05047 Manturov, Vassily Olegovich 1 2011 Parity in knot theory. Zbl 1210.57010 Manturov, V. O. 74 2010 Free knots and groups. Zbl 1195.57018 Manturov, O. V.; Manturov, V. O. 19 2010 Free knots and groups. Zbl 1261.57006 Manturov, V. O.; Manturov, O. V. 4 2010 Introduction to graph-link theory. Zbl 1189.57006 Ilyutko, Denis Petrovich; Manturov, Vassily Olegovich 11 2009 On virtual crossing number estimates for virtual links. Zbl 1183.57002 Afanasiev, Denis Mikhailovich; Manturov, Vassily Olegovich 7 2009 Graph-links. Zbl 1180.57012 Il’yutko, D. P.; Manturov, V. O. 6 2009 Cobordisms of free knots. Zbl 1196.57005 Il’yutko, D. P.; Manturov, V. O. 6 2009 Embeddings of 4-valent framed graphs into 2-surfaces. Zbl 1309.05054 Manturov, V. O. 5 2009 On minimal virtual link diagrams. Zbl 1176.57005 Afanasiev, D. M.; Manturov, V. O. 1 2009 Additional gradings in Khovanov homology. Zbl 1233.57007 Manturov, Vassily Olegovich 4 2008 Compact and long virtual knots. Zbl 1206.57008 Manturov, V. O. 4 2008 Additional gradings in the Khovanov complex for thickened surfaces. Zbl 1151.57303 Manturov, V. O. 2 2008 Khovanov homology for virtual knots with arbitrary coefficients. Zbl 1117.57013 Manturov, Vassily Olegovich 20 2007 Khovanov homology for virtual knots with arbitrary coefficients. Zbl 1142.57007 Manturov, V. O. 13 2007 The Khovanov complex for virtual links. Zbl 1165.57012 Manturov, V. O. 6 2007 Virtual knots and links. Zbl 1351.57012 Kauffman, L. H.; Manturov, V. O. 17 2006 The Khovanov complex and minimal knot diagrams. Zbl 1155.57303 Manturov, V. O. 6 2006 Virtual knot theory – unsolved problems. Zbl 1084.57005 Fenn, Roger; Kauffman, Louis H.; Manturov, Vassily O. 32 2005 Virtual biquandles. Zbl 1088.57006 Kauffman, Louis H.; Manturov, Vassily O. 29 2005 A proof of Vassiliev’s conjecture on the planarity of singular links. Zbl 1122.05030 Manturov, V. O. 12 2005 Vassiliev invariants for virtual links, curves on surfaces and the Jones-Kauffman polynomial. Zbl 1071.57011 Manturov, Vassily O. 8 2005 Recognition of virtual braids. Zbl 1144.20310 Manturov, V. O. 6 2005 Invariant tensor formulas via chord diagrams. Zbl 1146.57016 Campoamor-Stursberg, R.; Manturov, V. O. 6 2005 On long virtual knots. Zbl 1272.57005 Manturov, V. O. 4 2005 Flat hierarchy. Zbl 1088.57009 Manturov, Vassily O. 2 2005 Knot theory. Zbl 1052.57001 Manturov, Vassily 31 2004 Long virtual knots and their invariants. Zbl 1064.57005 Manturov, Vassily O. 18 2004 On polynomial invariants of virtual links. Zbl 1169.57302 Manturov, V. O. 5 2004 Virtual knots and infinite-dimensional Lie algebras. Zbl 1065.57005 Manturov, Vassily O. 2 2004 Finite-type invariants of virtual links and the Jones-Kauffman polynomial. Zbl 1282.57018 Manturov, V. O. 1 2004 Kauffman-like polynomial and curves in 2-surfaces. Zbl 1059.57006 Manturov, Vassily O. 14 2003 Multi-variable polynomial invariants for virtual links. Zbl 1061.57013 Manturov, Vassily O. 10 2003 Atoms and minimal diagrams of virtual links. Zbl 1125.57300 Manturov, V. O. 9 2003 Curves on surfaces virtual knots, and the Jones-Kaufmann polynomial. Zbl 1247.57011 Manturov, Vassily Olegovich 3 2003 On invariants of virtual links. Zbl 1003.57005 Manturov, V. O. 22 2002 A combinatorial representation of links by quasitoric braids. Zbl 0991.57007 Manturov, V. O. 6 2002 Invariants of virtual links. Zbl 1197.57014 Manturov, V. O. 4 2002 Chord diagrams and invariant tensors. Zbl 1014.57010 Manturov, Vassily O. 2 2002 Knots and the bracket calculus. Zbl 1014.57003 Manturov, V. O. 2 2002 On the recognition of braids. Zbl 1040.57009 Gaifullin, Alexander A.; Manturov, Vassily O. 2 2002 An invariant polynomial of two variables for virtual links. Zbl 1044.57003 Manturov, V. O. 1 2002 Maximally symmetric atoms and \(2 \times 2\) matrix groups. Zbl 1025.37015 Manturov, V. O. 2 2001 Bifurcations, atoms and knots. Zbl 0979.37028 Manturov, V. O. 10 2000 The bracket semigroup of knots. Zbl 0958.57010 Manturov, V. O. 2 2000 all cited Publications top 5 cited Publications all top 5 Cited by 297 Authors 69 Manturov, Vassiliĭ Olegovich 27 Kauffman, Louis Hirsch 18 Nikonov, Igor Mikhailovich 14 Chrisman, Micah Whitney 14 Im, Young Ho 14 Nelson, Sam 12 Boden, Hans U. 12 Dye, Heather Ann 11 Il’yutko, Denis Petrovich 10 Fedoseev, Denis Aleksandrovich 9 Cheng, Zhiyun 9 Kim, Sera 8 Bardakov, Valeriĭ Georgievich 8 Traldi, Lorenzo 7 Kim, Seongjeong 6 Gao, Hongzhu 6 Lee, Kyeonghui 6 Lee, Sang Youl 6 Rushworth, William 5 Bartholomew, Andrew 5 Jeong, Myeong-Ju 5 Kaestner, Aaron M. 5 Kamada, Naoko 5 Kamada, Seiichi 5 Karimi, Homayun 5 Park, Kyoung Il 5 Xu, Mengjian 4 Dasbach, Oliver T. 4 Lowrance, Adam M. 4 Nasybullov, Timur Rinatovich 4 Neshchadim, Mikhail Vladimirovich 4 Zenkina, M. V. 3 Afanasiev, Denis Mikhailovich 3 AlHussein, Hassan 3 Champanerkar, Abhijit 3 Gügümcü, Neslihan 3 Horvat, Eva 3 Ito, Noboru 3 Kim, Joonoh 3 Kofman, Ilya 3 Manturov, Oleg V. 3 Miyazawa, Yasuyuki 3 Nicas, Andrew J. 3 Stoltzfus, Neal W. 3 Vesnin, Andrei Yu. 2 Adams, Colin C. 2 Akimova, Alena Andreevna 2 Andersen, Jørgen Ellegaard 2 Baldridge, Scott Jeremy 2 Cattabriga, Alessia 2 Deng, Qingying 2 Emelyanenkov, Ivan Aleksandrovich 2 Fenn, Roger A. 2 Fukunaga, Tomonori 2 Gaudreau, Anne Isabel 2 Gaudreau, Robin 2 Gibson, Andrew 2 Greenberg, Jonah 2 Grishanov, Sergei A. 2 Harper, Eric 2 Hayashi, Chuichiro 2 Hayashi, Miwa 2 Ivanov, Maxim E. 2 Jang, Hee Jeong 2 Jin, Xian’an 2 Khan, Noureen A. 2 Lee, Sunho 2 Matveev, Sergeĭ Vladimirovich 2 Mikhalchishina, Yuliya A. 2 Miller, Kyle A. 2 Mishra, Rama 2 Morozov, Alexei Yurievich 2 Niebrzydowski, Maciej 2 Nowik, Tahl 2 Ogasa, Eiji 2 Penner, Robert C. 2 Satoh, Shin 2 Schrijver, Alexander 2 Seo, Myoungsoo 2 Tarkaev, Vladimir Viktorovich 2 Trifonova, V. A. 2 Turaev, Vladimir Georgievich 2 Vasil’ev, Viktor Anatol’evich 2 Vernitski, Alexei 2 Wan, Zheyan 2 White, Lindsay 1 Abe, Tetsuya 1 Abel, Michael 1 Abernathy, Susan M. 1 Acan, Hüseyin 1 Aggarwal, Laira 1 Alexeev, Nikita V. 1 Altintas, Ismet 1 Anashin, Vladimir Sergeevich 1 Armond, Cody W. 1 Bae, Yongju 1 Barrett, John William 1 Beldon, Theo 1 Bellingeri, Paolo 1 Benioff, Isaac ...and 197 more Authors all top 5 Cited in 70 Serials 167 Journal of Knot Theory and its Ramifications 21 Topology and its Applications 13 Algebraic & Geometric Topology 12 Journal of Mathematical Sciences (New York) 9 Proceedings of the American Mathematical Society 8 European Journal of Combinatorics 8 Doklady Mathematics 7 Moscow University Mathematics Bulletin 4 Mathematical Notes 4 International Journal of Mathematics 3 Fundamenta Mathematicae 3 Osaka Journal of Mathematics 3 Siberian Mathematical Journal 3 Transactions of the American Mathematical Society 3 Transactions of the Moscow Mathematical Society 3 Proceedings of the Steklov Institute of Mathematics 2 Communications in Mathematical Physics 2 Discrete Mathematics 2 Theoretical and Mathematical Physics 2 Geometriae Dedicata 2 Journal of Combinatorial Theory. Series B 2 Discrete & Computational Geometry 2 Annales Mathématiques Blaise Pascal 2 The New York Journal of Mathematics 2 Lobachevskii Journal of Mathematics 2 Mediterranean Journal of Mathematics 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Quantum Topology 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Bulletin of the Australian Mathematical Society 1 Discrete Applied Mathematics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Russian Mathematical Surveys 1 Beiträge zur Algebra und Geometrie 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Dissertationes Mathematicae 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Pure and Applied Algebra 1 Kyungpook Mathematical Journal 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Semigroup Forum 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Annals of Physics 1 Linear Algebra and its Applications 1 Experimental Mathematics 1 Combinatorics, Probability and Computing 1 Sbornik: Mathematics 1 Journal of Group Theory 1 New Journal of Physics 1 Communications in Contemporary Mathematics 1 Nihonkai Mathematical Journal 1 Journal of Algebra and its Applications 1 International Journal of Quantum Information 1 Applications and Applied Mathematics 1 Journal of Topology 1 Involve 1 East Asian Mathematical Journal 1 Science China. Mathematics 1 Bulletin of Mathematical Sciences 1 Open Mathematics all top 5 Cited in 31 Fields 321 Manifolds and cell complexes (57-XX) 38 Combinatorics (05-XX) 34 Group theory and generalizations (20-XX) 8 Associative rings and algebras (16-XX) 8 Algebraic topology (55-XX) 7 Category theory; homological algebra (18-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Quantum theory (81-XX) 5 Algebraic geometry (14-XX) 5 Nonassociative rings and algebras (17-XX) 5 Computer science (68-XX) 4 Differential geometry (53-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Commutative algebra (13-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Convex and discrete geometry (52-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Biology and other natural sciences (92-XX) Citations by Year