Edit Profile (opens in new tab) Turaev, Vladimir Georgievich Co-Author Distance Author ID: turaev.vladimir-g Published as: Turaev, Vladimir; Turaev, V. G.; Turaev, Vladimir G.; Turaev, V. more...less Further Spellings: Тураев Владимир Георгиевич Homepage: https://math.indiana.edu/about/faculty/touraev-vladimir.html External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 169 Publications since 1975, including 11 Books and 13 Additional arXiv Preprints 3 Contributions as Editor · 1 Further Contribution Reviewing Activity: 1 Review Biographic References: 2 Publications Co-Authors: 93 Co-Authors with 64 Joint Publications 2,341 Co-Co-Authors all top 5 Co-Authors 107 single-authored 7 Virelizier, Alexis 6 Kassel, Christian 5 Massuyeau, Gwénaël 4 Geer, Nathan 3 Andersen, Jørgen Ellegaard 3 Cimasoni, David 3 Fenn, Roger Andrew 3 Fominykh, Evgeny Anatol’evich 3 Le, Thang Tu Quoc 3 Matveev, Sergeĭ Vladimirovich 3 Patureau-Mirand, Bertrand 3 Vesnin, Andrei Yu. 3 Viro, Oleg Ya. 2 Deloup, Florian L. 2 Farber, Michael S. 2 Frenkel, Igor B. 2 Jones, Vaughan Frederick Randal 2 Kashaev, Rinat M. 2 Kerler, Thomas 2 Kohno, Toshitake 2 Murakami, Jun 2 Natanzon, Sergei M. 2 Ohtsuki, Tomotada 2 Przytycki, Józef Henryk 2 Reshetikhin, Nikolai Yu. 2 Roberts, Justin 2 Rosso, Marc 2 Vainerman, Leonid I. 2 Wenzl, Hans 1 Bar-Natan, Dror 1 Bartholomew, Andy 1 Baseilhac, Stéphane 1 Benedetti, Riccardo 1 Bespalov, Yuri N. 1 Boileau, Michel Charles 1 Budden, Steve 1 Bukhshtaber, Viktor Matveevich 1 Carter, J. Scott 1 Chen, Beifang 1 Chernavskiĭ, Alekseĭ Viktorovich 1 Costantino, Francesco 1 Dodane, Olivier 1 Dunfield, Nathan M. 1 Dynnikov, Ivan Alekseevich 1 Ferrand, Emmanuel 1 Fomenko, Anatoliĭ Timofeevich 1 Garoufalidis, Stavros 1 Gómez Larrañaga, José Carlos 1 González Acuña, Francisco Javier 1 Goussarov, Mikhail 1 Graña, Matías 1 Guadagnini, Enore 1 Habiro, H. 1 Hansen, Søren Kold 1 Harikae, Toshio 1 Ivanov, V. N. 1 Kania-Bartoszyńska, Joanna 1 Kawahigashi, Yasuyuki 1 Kharlamov, Viatcheslav M. 1 Kidwell, Mark Elliot 1 King, Simon A. 1 Kricker, Andrew 1 Kuno, Yusuke 1 Lescop, Christine 1 Lyubashenko, Volodymyr V. 1 Masbaum, Gregor 1 Mnëv, Nikolai Evgen’evich 1 Morton, Hugh R. 1 Müger, Michael 1 Murakami, Hitoshi 1 Nakanishi, Yasutaka 1 Natapov, Michael 1 Nikshych, Dmitri 1 Ohyama, Yoshiyuki 1 Okamoto, Miyuki 1 Okuda, Nobuki 1 Penner, Robert C. 1 Pilo, Luigi 1 Polyak, Michael 1 Porter, Timothy 1 Reshetnyak, Yuriĭ Grigor’evich 1 Rourke, Colin P. 1 Rozansky, Lev 1 Sanderson, Brian J. 1 Sato, Nobuya 1 Schlenk, Felix 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Staic, Mihai D. 1 Stanford, Theodore B. 1 Stoimenow, Alexander 1 Taĭmanov, Iskander Asanovich 1 Takata, Toshie 1 Tarkaev, Vladimir Viktorovich 1 Thurston, Dylan Paul 1 Traczyk, Paweł 1 Vasil’ev, Viktor Anatol’evich 1 Vershik, Anatoliĭ Moiseevich 1 Willerton, Simon 1 Yokota, Yoshiyuki all top 5 Serials 9 Journal of Soviet Mathematics 9 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 8 Mathematics of the USSR, Sbornik 6 Matematicheskiĭ Sbornik. Novaya Seriya 5 Journal of Geometry and Physics 4 Journal of Pure and Applied Algebra 4 International Journal of Mathematics 4 Algebraic & Geometric Topology 3 Advances in Mathematics 3 Journal of Algebra 3 Topology 3 L’Enseignement Mathématique. 2e Série 3 Mathematical Research Letters 3 De Gruyter Studies in Mathematics 2 Communications in Mathematical Physics 2 Russian Mathematical Surveys 2 Annales de l’Institut Fourier 2 Functional Analysis and its Applications 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Geometriae Dedicata 2 Inventiones Mathematicae 2 Journal für die Reine und Angewandte Mathematik 2 Mathematics of the USSR. Izvestiya 2 Osaka Journal of Mathematics 2 Pacific Journal of Mathematics 2 Soviet Mathematics. Doklady 2 Topology and its Applications 2 IMRN. International Mathematics Research Notices 2 Journal of Knot Theory and its Ramifications 2 Progress in Mathematics 1 International Journal of Modern Physics B 1 Discrete Mathematics 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Matematicheskie Zametki 1 Acta Mathematica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Fundamenta Mathematicae 1 Publications Mathématiques 1 Journal of Differential Geometry 1 Mathematische Annalen 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Leningrad Mathematical Journal 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Matematicheskiĭ Sbornik 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Sbornik: Mathematics 1 Doklady Mathematics 1 The Arabian Journal for Science and Engineering. Section C: Theme Issues 1 Communications in Contemporary Mathematics 1 Moscow Mathematical Journal 1 Banach Center Publications 1 Graduate Texts in Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 Panoramas et Synthèses 1 Geometry and Topology Monographs 1 Journal of Noncommutative Geometry 1 Journal of Homotopy and Related Structures 1 Journal of Topology 1 EMS Tracts in Mathematics 1 Japanese Journal of Mathematics. 3rd Series 1 Quantum Topology 1 Kyoto Journal of Mathematics 1 Translations. Series 2. American Mathematical Society all top 5 Fields 140 Manifolds and cell complexes (57-XX) 33 Quantum theory (81-XX) 29 Nonassociative rings and algebras (17-XX) 26 Category theory; homological algebra (18-XX) 24 Group theory and generalizations (20-XX) 24 Algebraic topology (55-XX) 11 Associative rings and algebras (16-XX) 7 Number theory (11-XX) 5 Combinatorics (05-XX) 5 Differential geometry (53-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Topological groups, Lie groups (22-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 3 General topology (54-XX) 2 Algebraic geometry (14-XX) 2 \(K\)-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Functional analysis (46-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 138 Publications have been cited 4,495 times in 2,932 Documents Cited by ▼ Year ▼ Invariants of 3-manifolds via link polynomials and quantum groups. Zbl 0725.57007 Reshetikhin, N.; Turaev, V. G. 598 1991 Quantum invariants of knots and 3-manifolds. Zbl 0812.57003 Turaev, V. G. 467 1994 Ribbon graphs and their invariants derived from quantum groups. Zbl 0768.57003 Reshetikhin, N. Yu.; Turaev, V. G. 448 1990 State sum invariants of 3-manifolds and quantum \(6j\)-symbols. Zbl 0779.57009 Turaev, V. G.; Viro, O. Y. 394 1992 The Yang-Baxter equation and invariants of links. Zbl 0648.57003 Turaev, V. G. 222 1988 Braid groups. With the graphical assistance of Olivier Dodane. Zbl 1208.20041 Kassel, Christian; Turaev, Vladimir 179 2008 Introduction to combinatorial torsions. Notes taken by Felix Schlenk. Zbl 0970.57001 Turaev, V. G. 112 2001 Skein quantization of Poisson algebras of loops on surfaces. Zbl 0758.57011 Turaev, Vladimir G. 109 1991 Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier. Zbl 1243.81016 Turaev, Vladimir 93 2010 Reidemeister torsion in knot theory. Zbl 0602.57005 Turaev, V. G. 83 1986 Quantum invariants of knots and 3-manifolds. 3rd edition. Zbl 1346.57002 Turaev, Vladimir G. 71 2016 Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016 Frenkel, Igor B.; Turaev, Vladimir G. 71 1997 Quantum invariants of knots and 3-manifolds. 2nd revised ed. Zbl 1213.57002 Turaev, Vladimir G. 68 2010 Monoidal categories and topological field theory. Zbl 1423.18001 Turaev, Vladimir; Virelizier, Alexis 65 2017 Torsions of 3-dimensional manifolds. Zbl 1012.57002 Turaev, V. 58 2002 Virtual strings. Zbl 1066.57022 Turaev, Vladimir 58 2004 Invariants of knots and 3-manifolds from quantum groupoids. Zbl 1021.16026 Nikshych, Dmitri; Turaev, Vladimir; Vainerman, Leonid 55 2003 Torsion invariants of Spin\(^c\)-structures on 3-manifolds. Zbl 0891.57019 Turaev, Vladimir 55 1997 Operator invariants of tangles, and R-matrices. Zbl 0707.57003 Turaev, V. G. 52 1990 The Conway and Kauffman modules of the solid torus. Zbl 0673.57004 Turaev, V. G. 51 1988 Modified quantum dimensions and re-normalized link invariants. Zbl 1160.81022 Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 51 2009 Knotoids. Zbl 1271.57030 Turaev, Vladimir 50 2012 Quantum invariants of 3-manifolds associated with classical simple Lie algebras. Zbl 0784.57007 Turaev, V.; Wenzl, H. 43 1993 Conway and Kauffman modules of a solid torus. Zbl 0706.57004 Turaev, V. G. 43 1990 Euler structures, nonsingular vector fields, and torsions of Reidemeister type. Zbl 0692.57015 Turaev, V. G. 42 1990 A simple proof of the Murasugi and Kauffman theorems on alternating links. Zbl 0668.57009 Turaev, V. G. 35 1987 Modular categories and 3-manifold invariants. Zbl 0798.57002 Turaev, Vladimir G. 33 1992 Topology of words. Zbl 1145.57018 Turaev, Vladimir 33 2007 Quantum groups and knot invariants. Zbl 0878.17013 Kassel, Christian; Rosso, Marc; Turaev, Vladimir 31 1997 Integrals for braided Hopf algebras. Zbl 0961.16023 Bespalov, Yuri; Kerler, Thomas; Lyubashenko, Volodymyr; Turaev, Vladimir 28 2000 Crossed group-categories. Zbl 1185.18009 Turaev, Vladimir 27 2008 Cobordism of knots on surfaces. Zbl 1166.57008 Turaev, Vladimir 27 2008 Quasi-Poisson structures on representation spaces of surfaces. Zbl 1298.53085 Massuyeau, Gwénaël; Turaev, Vladimir 26 2014 Shadow links and face models of statistical mechanics. Zbl 0773.57012 Turaev, Vladimir G. 26 1992 Poincaré-Reidemeister metric, Euler structures, and torsion. Zbl 0938.57020 Farber, Michael; Turaev, Vladimir 23 2000 Unoriented topological quantum field theory and link homology. Zbl 1134.57004 Turaev, Vladimir; Turner, Paul 22 2006 A combinatorial formulation for the Seiberg-Witten invariants of 3-manifolds. Zbl 1002.57036 Turaev, Vladimir 21 1998 On 3-dimensional homotopy quantum field theory. I. Zbl 1254.57012 Turaev, Vladimir; Virelizier, Alexis 21 2012 Semisimple and modular categories from link invariants. Zbl 0888.18001 Turaev, Vladimir; Wenzl, Hans 18 1997 Double construction for monoidal categories. Zbl 0833.18005 Kassel, Christian; Turaev, Vladimir 17 1995 Milnor invariants and Massey products. Zbl 0354.55013 Turaev, V. G. 17 1976 On reciprocity. Zbl 1167.11030 Deloup, Florian; Turaev, Vladimir 16 2007 On 3-dimensional homotopy quantum field theory II: the surgery approach. Zbl 1296.57016 Turaev, Vladimir; Virelizier, Alexis 16 2014 Weyl algebras and knots. Zbl 1123.57006 Fenn, Roger; Turaev, Vladimir 15 2007 On 3-dimensional homotopy quantum field theory III: comparison of two approaches. Zbl 1473.57032 Turaev, Vladimir; Virelizier, Alexis 14 2020 Lectures on topology of words. Zbl 1162.68034 Turaev, Vladimir 13 2007 Fox pairings and generalized Dehn twists. (Formes de Fox et twists de Dehn généralisés.) Zbl 1297.57005 Massuyeau, Gwénaël; Turaev, Vladimir 12 2013 Modified \(6j\)-symbols and 3-manifold invariants. Zbl 1237.57011 Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 12 2011 The Alexander polynomial of a 3-dimensional manifold. Zbl 0315.57001 Turaev, V. G. 11 1975 Torsions of \(3\)-manifolds. Zbl 1012.57034 Turaev, Vladimir 11 2002 Biquantization of Lie bialgebras. Zbl 1040.17008 Kassel, Christian; Turaev, Vladimir 11 2000 Quantum invariants of 3-manifolds and a glimpse of shadow topology. Zbl 0752.57009 Turaev, Vladimir 10 1991 Intersections of loops in two-dimensional manifolds. Zbl 0422.57005 Turaev, V. G. 10 1979 Chord diagram invariants of tangles and graphs. Zbl 0947.57010 Kassel, Christian; Turaev, Vladimir 10 1998 Faithful linear representations of the braid groups. Zbl 1050.20026 Turaev, Vladimir 10 2002 A Lagrangian representation of tangles. Zbl 1071.57006 Cimasoni, David; Turaev, Vladimir 10 2005 A generalization of several classical invariants of links. Zbl 1148.57005 Cimasoni, David; Turaev, Vladimir 10 2007 Dijkgraaf-Witten invariants of surfaces and projective representations of groups. Zbl 1163.57021 Turaev, Vladimir 10 2007 On the graded center of graded categories. Zbl 1301.18012 Turaev, Vladimir; Virelizier, Alexis 9 2013 Quantum invariants of links and 3-valent graphs in 3-manifolds. Zbl 0822.57012 Turaev, Vladimir 9 1993 A norm for the cohomology of 2-complexes. Zbl 1014.57002 Turaev, Vladimir 9 2002 Cohomology rings, linking forms and invariants of spin structures of three-dimensional manifolds. Zbl 0553.57004 Turaev, V. G. 9 1984 Tetrahedral forms in monoidal categories and 3-manifold invariants. Zbl 1261.57013 Geer, Nathan; Kashaev, Rinat; Turaev, Vladimir 9 2012 Knots and words. Zbl 1118.57009 Turaev, Vladimir 9 2006 Classification of oriented Montesinos links via spin structures. Zbl 0648.57002 Turaev, V. G. 8 1988 Reidemeister torsion and the Alexander polynomial. Zbl 0381.57003 Turaev, V. G. 8 1978 Schnitte von Schleifen in zweidimensionalen Mannigfaltigkeiten. Zbl 0384.57004 Turaev, V. G. 8 1978 Absolute torsion. Zbl 0934.57030 Farber, Michael; Turaev, Vladimir 8 1999 A compactification of the Hurwitz space. Zbl 0929.57001 Natanzon, Sergei; Turaev, Vladimir 8 1999 Formal homotopy quantum field theories. I: Formal maps and crossed \(\mathcal{C}\)-algebras. Zbl 1205.57024 Porter, Timothy; Turaev, Vladimir 8 2008 Milnor invariants and Massay products. Zbl 0406.55017 Turaev, V. G. 7 1979 Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0732.57008 Turaev, V. G. 7 1989 Reciprocity for Gauss sums on finite Abelian groups. Zbl 1048.11501 Turaev, Vladimir 7 1998 A cocycle for the symplectic first Chern class and Maslov indices. Zbl 0556.55012 Turaev, V. G. 7 1984 Cohomology ring forms of linking coefficients and invariants of spinor structures in three-dimensional manifolds. Zbl 0519.57009 Turaev, V. G. 7 1983 A semigroup of theta-curves in 3-manifolds. Zbl 1284.57012 Matveev, Sergei; Turaev, Vladimir 7 2011 Nilpotent homotopy types of closed 3-manifolds. Zbl 0564.57008 Turaev, V. G. 6 1984 A cocycle for the symplectic first Chern class and the Maslov index. Zbl 0577.55011 Turaev, V. G. 6 1984 Quantum groups and ribbon \(G\)-categories. Zbl 1035.57006 Le, Thang; Turaev, Vladimir 6 2003 Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0693.57013 Turaev, V. G. 6 1989 Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0717.57008 Turaev, V. G. 6 1990 First symplectic Chern class and Maslov indices. Zbl 0612.55019 Turaev, V. G. 6 1987 Quantum invariants of 3-manifold and a glimpse of shadow topology. Zbl 0752.57010 Turaev, Vladimir 5 1992 State sum models in low-dimensional topology. Zbl 0744.57007 Turaev, Vladimir G. 5 1991 On the definition of the 2-category of 2-knots. Zbl 0851.18003 Kharlamov, V. M.; Turaev, V. G. 5 1996 Loops on surfaces, Feynman diagrams, and trees. Zbl 1094.57022 Turaev, Vladimir 5 2005 Curves on surfaces, charts, and words. Zbl 1126.57010 Turaev, Vladimir 5 2005 A function on the homology of 3-manifolds. Zbl 1145.57011 Turaev, Vladimir 5 2007 A canonical cocycle for the Euler class of a flat vector bundle. Zbl 0518.57012 Ivanov, V. N.; Turaev, V. G. 5 1982 Homeomorphisms of geometric three-dimensional manifolds. Zbl 0659.57007 Turaev, V. G. 4 1988 The Alexander polynomial of a three-dimensional manifold. Zbl 0339.57002 Turaev, V. G. 4 1976 Die Reidemeistersche Torsion und das Alexandersche Polynom. Zbl 0364.57004 Turaev, V. G. 4 1976 Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024 Frenkel, Igor B.; Turaev, Vladimir G. 4 1995 Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0853.57016 Turaev, V. G. 4 1994 Kuperberg and Turaev-Viro invariants in unimodular categories. Zbl 1454.18014 Costantino, Francesco; Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 4 2020 On certain enumeration problems in two-dimensional topology. Zbl 1175.57013 Turaev, Vladimir 4 2009 Intersections of loops in two-dimensional manifolds. II: Free loops. Zbl 0543.57007 Turaev, V. G.; Viro, O. Ya. 4 1984 The first symplectic Chern class and the Maslov indices. Zbl 0577.55012 Turaev, V. G. 3 1985 Complexity of virtual 3-manifolds. Zbl 1362.57028 Vesnin, Andrei Yu.; Turaev, Vladimir G.; Fominykh, Evgeny A. 3 2016 Towards the topological classification of geometric 3-manifolds. Zbl 0651.57011 Turaev, V. G. 3 1988 Topological constructions of tensor fields on moduli spaces. Zbl 1481.57023 Turaev, Vladimir 3 2021 Loops in surfaces and star-fillings. Zbl 1497.55009 Turaev, Vladimir 2 2021 On 3-dimensional homotopy quantum field theory III: comparison of two approaches. Zbl 1473.57032 Turaev, Vladimir; Virelizier, Alexis 14 2020 Kuperberg and Turaev-Viro invariants in unimodular categories. Zbl 1454.18014 Costantino, Francesco; Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 4 2020 Quasi-Poisson structures on moduli spaces of quasi-surfaces. Zbl 1495.17034 Turaev, Vladimir 1 2020 Brackets in representation algebras of Hopf algebras. Zbl 1464.17026 Massuyeau, Gwénaël; Turaev, Vladimir 1 2018 Trimming of metric spaces and the tight span. Zbl 1402.54029 Turaev, Vladimir 1 2018 Monoidal categories and topological field theory. Zbl 1423.18001 Turaev, Vladimir; Virelizier, Alexis 65 2017 Brackets in the Pontryagin algebras of manifolds. (Crochets dans les algèbres de Pontryagin des variétés.) Zbl 1416.17012 Massuyeau, Gwénaël; Turaev, Vladimir 2 2017 Quantum invariants of knots and 3-manifolds. 3rd edition. Zbl 1346.57002 Turaev, Vladimir G. 71 2016 Complexity of virtual 3-manifolds. Zbl 1362.57028 Vesnin, Andrei Yu.; Turaev, Vladimir G.; Fominykh, Evgeny A. 3 2016 Three-dimensional manifolds with poor spines. Zbl 1328.57026 Vesnin, A. Yu.; Turaev, V. G.; Fominykh, E. A. 2 2015 Dijkgraaf-Witten invariants over \(\mathbb Z_2\) for 3-manifolds. Zbl 1327.57019 Matveev, S. V.; Turaev, V. G. 2 2015 Quasi-Poisson structures on representation spaces of surfaces. Zbl 1298.53085 Massuyeau, Gwénaël; Turaev, Vladimir 26 2014 On 3-dimensional homotopy quantum field theory II: the surgery approach. Zbl 1296.57016 Turaev, Vladimir; Virelizier, Alexis 16 2014 Poisson-Gerstenhaber brackets in representation algebras. Zbl 1308.17027 Turaev, Vladimir 3 2014 Fox pairings and generalized Dehn twists. (Formes de Fox et twists de Dehn généralisés.) Zbl 1297.57005 Massuyeau, Gwénaël; Turaev, Vladimir 12 2013 On the graded center of graded categories. Zbl 1301.18012 Turaev, Vladimir; Virelizier, Alexis 9 2013 Marked fatgraph complexes and surface automorphisms. Zbl 1367.57012 Kuno, Yusuke; Penner, R. C.; Turaev, Vladimir 2 2013 Knotoids. Zbl 1271.57030 Turaev, Vladimir 50 2012 On 3-dimensional homotopy quantum field theory. I. Zbl 1254.57012 Turaev, Vladimir; Virelizier, Alexis 21 2012 Tetrahedral forms in monoidal categories and 3-manifold invariants. Zbl 1261.57013 Geer, Nathan; Kashaev, Rinat; Turaev, Vladimir 9 2012 Modified \(6j\)-symbols and 3-manifold invariants. Zbl 1237.57011 Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 12 2011 A semigroup of theta-curves in 3-manifolds. Zbl 1284.57012 Matveev, Sergei; Turaev, Vladimir 7 2011 Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier. Zbl 1243.81016 Turaev, Vladimir 93 2010 Quantum invariants of knots and 3-manifolds. 2nd revised ed. Zbl 1213.57002 Turaev, Vladimir G. 68 2010 Remarks on 2-dimensional HQFTs. Zbl 1226.57043 Staic, Mihai D.; Turaev, Vladimir 3 2010 Enumeration of lifts of commuting elements of a group. Zbl 1214.20012 Natapov, Michael; Turaev, Vladimir 1 2010 Modified quantum dimensions and re-normalized link invariants. Zbl 1160.81022 Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir 51 2009 On certain enumeration problems in two-dimensional topology. Zbl 1175.57013 Turaev, Vladimir 4 2009 Braid groups. With the graphical assistance of Olivier Dodane. Zbl 1208.20041 Kassel, Christian; Turaev, Vladimir 179 2008 Crossed group-categories. Zbl 1185.18009 Turaev, Vladimir 27 2008 Cobordism of knots on surfaces. Zbl 1166.57008 Turaev, Vladimir 27 2008 Formal homotopy quantum field theories. I: Formal maps and crossed \(\mathcal{C}\)-algebras. Zbl 1205.57024 Porter, Timothy; Turaev, Vladimir 8 2008 Cobordisms of words. Zbl 1221.57032 Turaev, Vladimir 3 2008 Topology of words. Zbl 1145.57018 Turaev, Vladimir 33 2007 On reciprocity. Zbl 1167.11030 Deloup, Florian; Turaev, Vladimir 16 2007 Weyl algebras and knots. Zbl 1123.57006 Fenn, Roger; Turaev, Vladimir 15 2007 Lectures on topology of words. Zbl 1162.68034 Turaev, Vladimir 13 2007 A generalization of several classical invariants of links. Zbl 1148.57005 Cimasoni, David; Turaev, Vladimir 10 2007 Dijkgraaf-Witten invariants of surfaces and projective representations of groups. Zbl 1163.57021 Turaev, Vladimir 10 2007 A function on the homology of 3-manifolds. Zbl 1145.57011 Turaev, Vladimir 5 2007 Coalgebras of words and phrases. Zbl 1136.16037 Turaev, Vladimir 2 2007 Unoriented topological quantum field theory and link homology. Zbl 1134.57004 Turaev, Vladimir; Turner, Paul 22 2006 Knots and words. Zbl 1118.57009 Turaev, Vladimir 9 2006 A Lagrangian representation of tangles. II. Zbl 1106.57004 Cimasoni, David; Turaev, Vladimir 3 2006 A Lagrangian representation of tangles. Zbl 1071.57006 Cimasoni, David; Turaev, Vladimir 10 2005 Loops on surfaces, Feynman diagrams, and trees. Zbl 1094.57022 Turaev, Vladimir 5 2005 Curves on surfaces, charts, and words. Zbl 1126.57010 Turaev, Vladimir 5 2005 Knot theory for self-indexed graphs. Zbl 1074.57005 Graña, Matías; Turaev, Vladimir 1 2005 Virtual strings. Zbl 1066.57022 Turaev, Vladimir 58 2004 Invariants of knots and 3-manifolds from quantum groupoids. Zbl 1021.16026 Nikshych, Dmitri; Turaev, Vladimir; Vainerman, Leonid 55 2003 Quantum groups and ribbon \(G\)-categories. Zbl 1035.57006 Le, Thang; Turaev, Vladimir 6 2003 Torsions of 3-dimensional manifolds. Zbl 1012.57002 Turaev, V. 58 2002 Torsions of \(3\)-manifolds. Zbl 1012.57034 Turaev, Vladimir 11 2002 Faithful linear representations of the braid groups. Zbl 1050.20026 Turaev, Vladimir 10 2002 A norm for the cohomology of 2-complexes. Zbl 1014.57002 Turaev, Vladimir 9 2002 Invariants of knots and 3-manifolds. Proceedings of the workshop, Kyoto, Japan, September 17–21, 2001. Zbl 0996.00037 1 2002 Introduction to combinatorial torsions. Notes taken by Felix Schlenk. Zbl 0970.57001 Turaev, V. G. 112 2001 Topology, ergodic theory, real algebraic geometry. Rokhlin’s memorial. Zbl 0961.00011 2 2001 Higher skein modules. II. Zbl 1008.57011 Andersen, Jørgen Ellegaard; Turaev, Vladimir 1 2001 Integrals for braided Hopf algebras. Zbl 0961.16023 Bespalov, Yuri; Kerler, Thomas; Lyubashenko, Volodymyr; Turaev, Vladimir 28 2000 Poincaré-Reidemeister metric, Euler structures, and torsion. Zbl 0938.57020 Farber, Michael; Turaev, Vladimir 23 2000 Biquantization of Lie bialgebras. Zbl 1040.17008 Kassel, Christian; Turaev, Vladimir 11 2000 Counting lattice points of rational polyhedra. Zbl 0988.52020 Chen, Beifang; Turaev, Vladimir 1 2000 Absolute torsion. Zbl 0934.57030 Farber, Michael; Turaev, Vladimir 8 1999 A compactification of the Hurwitz space. Zbl 0929.57001 Natanzon, Sergei; Turaev, Vladimir 8 1999 Higher skein modules. Zbl 0991.57015 Andersen, Jørgen Ellegaard; Turaev, Vladimir 2 1999 A combinatorial formulation for the Seiberg-Witten invariants of 3-manifolds. Zbl 1002.57036 Turaev, Vladimir 21 1998 Chord diagram invariants of tangles and graphs. Zbl 0947.57010 Kassel, Christian; Turaev, Vladimir 10 1998 Reciprocity for Gauss sums on finite Abelian groups. Zbl 1048.11501 Turaev, Vladimir 7 1998 Systems of correlators and solutions of the WDVV equations. Zbl 0906.35098 Natanzon, Sergei; Turaev, Vladimir 2 1998 Knot theory. Proceedings of the mini-semester, Warsaw, Poland, July 13–August 17, 1995. Zbl 0890.00048 1 1998 Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016 Frenkel, Igor B.; Turaev, Vladimir G. 71 1997 Torsion invariants of Spin\(^c\)-structures on 3-manifolds. Zbl 0891.57019 Turaev, Vladimir 55 1997 Quantum groups and knot invariants. Zbl 0878.17013 Kassel, Christian; Rosso, Marc; Turaev, Vladimir 31 1997 Semisimple and modular categories from link invariants. Zbl 0888.18001 Turaev, Vladimir; Wenzl, Hans 18 1997 The Conway and Kauffman modules of the solid torus. Zbl 0928.57014 Turaev, Vladimir G. 3 1997 On the definition of the 2-category of 2-knots. Zbl 0851.18003 Kharlamov, V. M.; Turaev, V. G. 5 1996 Double construction for monoidal categories. Zbl 0833.18005 Kassel, Christian; Turaev, Vladimir 17 1995 Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024 Frenkel, Igor B.; Turaev, Vladimir G. 4 1995 Quantum invariants of knots and 3-manifolds. Zbl 0812.57003 Turaev, V. G. 467 1994 Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0853.57016 Turaev, V. G. 4 1994 Axioms for topological quantum field theories. Zbl 0797.53058 Turaev, Vladimir G. 1 1994 Quantum invariants of 3-manifolds associated with classical simple Lie algebras. Zbl 0784.57007 Turaev, V.; Wenzl, H. 43 1993 Quantum invariants of links and 3-valent graphs in 3-manifolds. Zbl 0822.57012 Turaev, Vladimir 9 1993 State sum invariants of 3-manifolds and quantum \(6j\)-symbols. Zbl 0779.57009 Turaev, V. G.; Viro, O. Y. 394 1992 Modular categories and 3-manifold invariants. Zbl 0798.57002 Turaev, Vladimir G. 33 1992 Shadow links and face models of statistical mechanics. Zbl 0773.57012 Turaev, Vladimir G. 26 1992 Quantum invariants of 3-manifold and a glimpse of shadow topology. Zbl 0752.57010 Turaev, Vladimir 5 1992 Invariants of 3-manifolds via link polynomials and quantum groups. Zbl 0725.57007 Reshetikhin, N.; Turaev, V. G. 598 1991 Skein quantization of Poisson algebras of loops on surfaces. Zbl 0758.57011 Turaev, Vladimir G. 109 1991 Quantum invariants of 3-manifolds and a glimpse of shadow topology. Zbl 0752.57009 Turaev, Vladimir 10 1991 State sum models in low-dimensional topology. Zbl 0744.57007 Turaev, Vladimir G. 5 1991 Ribbon graphs and their invariants derived from quantum groups. Zbl 0768.57003 Reshetikhin, N. Yu.; Turaev, V. G. 448 1990 Operator invariants of tangles, and R-matrices. Zbl 0707.57003 Turaev, V. G. 52 1990 Conway and Kauffman modules of a solid torus. Zbl 0706.57004 Turaev, V. G. 43 1990 Euler structures, nonsingular vector fields, and torsions of Reidemeister type. Zbl 0692.57015 Turaev, V. G. 42 1990 Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0717.57008 Turaev, V. G. 6 1990 Elementary ideals of links and manifolds: Symmetry and asymmetry. Zbl 0715.57003 Turaev, V. G. 1 1990 ...and 38 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,544 Authors 47 Turaev, Vladimir Georgievich 46 Kauffman, Louis Hirsch 38 Schweigert, Christoph 36 Le, Thang Tu Quoc 35 Runkel, Ingo 34 Geer, Nathan 33 Morozov, Alexei Yurievich 31 Garoufalidis, Stavros 29 Patureau-Mirand, Bertrand 29 Wang, Shuanhong 28 Rowell, Eric C. 28 Wang, Zhenghan 27 Mironov, Andrei D. 24 Morozov, Andreĭ Alekseevich 21 Manturov, Vassiliĭ Olegovich 20 Friedl, Stefan 20 Fuchs, Jürgen 17 Andersen, Jørgen Ellegaard 15 Costantino, Francesco 15 Dittrich, Bianca 15 Gukov, Sergei 15 Reshetikhin, Nikolai Yu. 14 Gilmer, Patrick M. 14 Massuyeau, Gwénaël 13 Hikami, Kazuhiro 13 Lambropoulou, Sofia S. F. 13 Przytycki, Józef Henryk 12 Gainutdinov, Azat M. 12 Kong, Liang 12 Murakami, Jun 12 Schlosser, Michael J. 12 Thuillier, Frank 12 Xu, Feng 11 Diamantis, Ioannis 11 Kadokami, Teruhisa 11 Kuno, Yusuke 11 Majid, Shahn 11 Ramadevi, Pichai 11 Spiridonov, Vyacheslav Pavlovich 11 Tarkaev, Vladimir Viktorovich 11 Virelizier, Alexis 11 Wenzl, Hans 11 Woike, Lukas 11 Wong, Helen M. 10 Beliakova, Anna 10 Chrisman, Micah Whitney 10 Delcamp, Clement 10 Freedman, Michael Hartley 10 Gabrovšek, Boštjan 10 Kashaev, Rinat M. 10 Meusburger, Catherine 10 Ramgoolam, Sanjaye 10 Rozansky, Lev 10 Saito, Masahico 9 Alonso Álvarez, José Nicanor 9 Blanchet, Christian 9 Creutzig, Thomas 9 Galindo Martínez, César Neyit 9 González Rodríguez, Ramón 9 Hillman, Jonathan Arthur 9 Jones, Corey 9 Khovanov, Mikhail G. 9 Livine, Etera R. 9 Matveev, Sergeĭ Vladimirovich 9 Mroczkowski, Maciej 9 Murakami, Hitoshi 9 Ng, Siu-Hung 9 Nikshych, Dmitri 9 Nosaka, Takefumi 9 Riello, Aldo 9 Savage, Alistair 9 Schaumann, Gregor 9 Shimizu, Kenichi 9 Zhang, Ruibin 8 Alekseev, Anton Yur’evich 8 Baez, John C. 8 Barrett, John William 8 Boden, Hans U. 8 Bonahon, Francis 8 Detcherry, Renaud 8 Evans, David E. 8 Freed, Daniel Stuart 8 Freidel, Laurent 8 Frohman, Charles D. 8 Gannon, Terry 8 Gavarini, Fabio 8 Gould, Mark D. 8 Gügümcü, Neslihan 8 Habiro, Kazuo 8 Hajij, Mustafa 8 Huang, Yi-Zhi 8 Im, Young Ho 8 Kitayama, Takahiro 8 Koda, Yuya 8 Laugwitz, Robert 8 Marché, Julien 8 Marzuoli, Annalisa 8 Masbaum, Gregor 8 Müller, Lukas 8 Nawata, Satoshi ...and 2,444 more Authors all top 5 Cited in 299 Serials 265 Journal of Knot Theory and its Ramifications 192 Communications in Mathematical Physics 131 Algebraic & Geometric Topology 112 Journal of High Energy Physics 103 Advances in Mathematics 103 Journal of Algebra 98 Journal of Mathematical Physics 74 Topology and its Applications 66 Transactions of the American Mathematical Society 60 Nuclear Physics. B 59 Journal of Pure and Applied Algebra 56 Journal of Geometry and Physics 51 Geometry & Topology 50 Quantum Topology 46 Letters in Mathematical Physics 42 Communications in Algebra 38 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 36 Proceedings of the American Mathematical Society 31 International Journal of Mathematics 30 Selecta Mathematica. New Series 25 Mathematical Proceedings of the Cambridge Philosophical Society 25 Journal of Physics A: Mathematical and Theoretical 24 Mathematische Annalen 23 Algebras and Representation Theory 23 Journal of Topology 22 Theoretical and Mathematical Physics 22 Duke Mathematical Journal 22 Communications in Contemporary Mathematics 21 Annals of Physics 19 Geometriae Dedicata 19 Applied Categorical Structures 19 Annales Henri Poincaré 18 Annales de l’Institut Fourier 18 Inventiones Mathematicae 18 Journal of Algebra and its Applications 16 Mathematische Zeitschrift 16 Bulletin of the American Mathematical Society. New Series 16 Theory and Applications of Categories 15 Classical and Quantum Gravity 14 Acta Mathematica Vietnamica 14 Osaka Journal of Mathematics 14 Journal of Mathematical Sciences (New York) 13 International Journal of Modern Physics A 13 Journal of the London Mathematical Society. Second Series 12 Israel Journal of Mathematics 12 Physics Letters. B 12 Reviews in Mathematical Physics 12 Manuscripta Mathematica 11 Compositio Mathematica 11 Indiana University Mathematics Journal 11 Journal of the American Mathematical Society 11 Transformation Groups 11 SciPost Physics 10 European Journal of Combinatorics 10 Experimental Mathematics 10 The Ramanujan Journal 9 Fundamenta Mathematicae 9 Pacific Journal of Mathematics 9 Siberian Mathematical Journal 9 Journal of Algebraic Combinatorics 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Winter Braids Lecture Notes 8 Discrete Mathematics 8 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 8 St. Petersburg Mathematical Journal 8 Mediterranean Journal of Mathematics 8 Journal of Noncommutative Geometry 7 Mathematical Notes 7 Memoirs of the American Mathematical Society 7 Proceedings of the London Mathematical Society. Third Series 7 Acta Mathematica Sinica. English Series 7 Proceedings of the Steklov Institute of Mathematics 7 Science China. Mathematics 6 General Relativity and Gravitation 6 Bulletin of the London Mathematical Society 6 Canadian Journal of Mathematics 6 Journal of Combinatorial Theory. Series A 6 Journal of the European Mathematical Society (JEMS) 6 Quantum Information Processing 6 Research in the Mathematical Sciences 6 Algebraic Combinatorics 5 Bulletin of the Australian Mathematical Society 5 Rocky Mountain Journal of Mathematics 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Journal für die Reine und Angewandte Mathematik 5 Journal of Soviet Mathematics 5 Tôhoku Mathematical Journal. Second Series 5 Tokyo Journal of Mathematics 5 Annales Mathématiques Blaise Pascal 5 Doklady Mathematics 5 International Journal of Geometric Methods in Modern Physics 5 Oberwolfach Reports 4 Modern Physics Letters A 4 Chaos, Solitons and Fractals 4 Bulletin de la Société Mathématique de France 4 Canadian Mathematical Bulletin 4 Glasgow Mathematical Journal 4 Journal of Combinatorial Theory. Series B 4 Journal of Differential Geometry ...and 199 more Serials all top 5 Cited in 56 Fields 1,641 Manifolds and cell complexes (57-XX) 869 Quantum theory (81-XX) 528 Category theory; homological algebra (18-XX) 499 Associative rings and algebras (16-XX) 490 Nonassociative rings and algebras (17-XX) 372 Group theory and generalizations (20-XX) 181 Global analysis, analysis on manifolds (58-XX) 169 Differential geometry (53-XX) 148 Algebraic geometry (14-XX) 140 Relativity and gravitational theory (83-XX) 133 Combinatorics (05-XX) 103 Functional analysis (46-XX) 94 Number theory (11-XX) 90 Algebraic topology (55-XX) 88 Special functions (33-XX) 81 Statistical mechanics, structure of matter (82-XX) 67 Topological groups, Lie groups (22-XX) 60 Dynamical systems and ergodic theory (37-XX) 47 Several complex variables and analytic spaces (32-XX) 35 Computer science (68-XX) 34 Commutative algebra (13-XX) 34 Linear and multilinear algebra; matrix theory (15-XX) 32 \(K\)-theory (19-XX) 26 Functions of a complex variable (30-XX) 18 Probability theory and stochastic processes (60-XX) 15 History and biography (01-XX) 15 Partial differential equations (35-XX) 14 Mechanics of particles and systems (70-XX) 14 Information and communication theory, circuits (94-XX) 13 General and overarching topics; collections (00-XX) 13 Geometry (51-XX) 12 Convex and discrete geometry (52-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Operator theory (47-XX) 10 Mathematical logic and foundations (03-XX) 9 Difference and functional equations (39-XX) 9 General topology (54-XX) 7 Field theory and polynomials (12-XX) 7 Abstract harmonic analysis (43-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 4 General algebraic systems (08-XX) 4 Statistics (62-XX) 4 Numerical analysis (65-XX) 4 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 3 Fluid mechanics (76-XX) 3 Operations research, mathematical programming (90-XX) 2 Ordinary differential equations (34-XX) 2 Sequences, series, summability (40-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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