# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 156 Publications since 1975, including 13 Books Reviewing Activity: 1 Review
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#### Co-Authors

 95 single-authored 6 Kassel, Christian 5 Virelizier, Alexis 4 Geer, Nathan 4 Massuyeau, Gwénaël 3 Cimasoni, David 3 Fominykh, Evgeny Anatol’evich 3 Matveev, Sergeĭ Vladimirovich 3 Patureau-Mirand, Bertrand 3 Vesnin, Andrei Yu. 2 Andersen, Jørgen Ellegaard 2 Farber, Michael S. 2 Frenkel, Igor B. 2 Le, Thang Tu Quoc 2 Natanzon, Sergei M. 2 Reshetikhin, Nikolai Yu. 2 Rosso, Marc 2 Vainerman, Leonid I. 2 Viro, Oleg Ya. 2 Wenzl, Hans 1 Bespalov, Yuri N. 1 Bukhshtaber, Viktor Matveevich 1 Chen, Beifang 1 Chernavskij, A. V. 1 Costantino, Francesco 1 Deloup, Florian L. 1 Dynnikov, Ivan Alekseevich 1 Fenn, Roger A. 1 Fomenko, Anatoliĭ Timofeevich 1 Gómez Larrañaga, José Carlos 1 González Acuña, Francisco Javier 1 Graña, Matías 1 Ivanov, V. N. 1 Jones, Vaughan Frederick Randal 1 Kania-Bartoszyńska, Joanna 1 Kashaev, Rinat M. 1 Kerler, Thomas 1 Kharlamov, Viatcheslav M. 1 King, Simon A. 1 Kohno, Toshitake 1 Kuno, Yusuke 1 Lyubashenko, Volodymyr V. 1 Murakami, Jun 1 Natapov, Michael 1 Nikshych, Dmitri 1 Ohtsuki, Tomotada 1 Penner, Robert C. 1 Porter, Timothy 1 Przytycki, Józef H. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Staic, Mihai D. 1 Taimanov, Iskander Asanovich 1 Tarkaev, Vladimir Viktorovich 1 Traczyk, Paweł 1 Vasil’ev, Viktor Anatol’evich 1 Vershik, Anatoliĭ Moiseevich
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#### 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 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 Advances in Mathematics 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 Translations. Series 2. American Mathematical Society
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#### Fields

 130 Manifolds and cell complexes (57-XX) 32 Quantum theory (81-XX) 27 Nonassociative rings and algebras (17-XX) 25 Category theory; homological algebra (18-XX) 22 Group theory and generalizations (20-XX) 22 Algebraic topology (55-XX) 11 Associative rings and algebras (16-XX) 7 Number theory (11-XX) 5 Differential geometry (53-XX) 4 Combinatorics (05-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Computer science (68-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Topological groups, Lie groups (22-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-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 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH Open

127 Publications have been cited 2,993 times in 1,984 Documents Cited by Year
Invariants of 3-manifolds via link polynomials and quantum groups. Zbl 0725.57007
Reshetikhin, N.; Turaev, V. G.
1991
Quantum invariants of knots and 3-manifolds. Zbl 0812.57003
Turaev, V. G.
1994
Ribbon graphs and their invariants derived from quantum groups. Zbl 0768.57003
Reshetikhin, N. Yu.; Turaev, V. G.
1990
State sum invariants of 3-manifolds and quantum $$6j$$-symbols. Zbl 0779.57009
Turaev, V. G.; Viro, O. Y.
1992
The Yang-Baxter equation and invariants of links. Zbl 0648.57003
Turaev, V. G.
1988
Introduction to combinatorial torsions. Notes taken by Felix Schlenk. Zbl 0970.57001
Turaev, V. G.
2001
Reidemeister torsion in knot theory. Zbl 0602.57005
Turaev, V. G.
1986
Braid groups. With the graphical assistance of Olivier Dodane. Zbl 1208.20041
2008
Skein quantization of Poisson algebras of loops on surfaces. Zbl 0758.57011
1991
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016
Frenkel, Igor B.; Turaev, Vladimir G.
1997
Virtual strings. Zbl 1066.57022
2004
Quantum invariants of knots and 3-manifolds. 2nd revised ed. Zbl 1213.57002
2010
Torsion invariants of Spin$$^c$$-structures on 3-manifolds. Zbl 0891.57019
1997
Invariants of knots and 3-manifolds from quantum groupoids. Zbl 1021.16026
Nikshych, Dmitri; Turaev, Vladimir; Vainerman, Leonid
2003
Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier. Zbl 1243.81016
2010
Quantum invariants of 3-manifolds associated with classical simple Lie algebras. Zbl 0784.57007
Turaev, V.; Wenzl, H.
1993
Torsions of 3-dimensional manifolds. Zbl 1012.57002
Turaev, V.
2002
Euler structures, nonsingular vector fields, and torsions of Reidemeister type. Zbl 0692.57015
Turaev, V. G.
1990
Operator invariants of tangles, and R-matrices. Zbl 0707.57003
Turaev, V. G.
1990
The Conway and Kauffman modules of the solid torus. Zbl 0673.57004
Turaev, V. G.
1988
Modified quantum dimensions and re-normalized link invariants. Zbl 1160.81022
Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir
2009
Topology of words. Zbl 1145.57018
2007
Quantum groups and knot invariants. Zbl 0878.17013
Kassel, Christian; Rosso, Marc; Turaev, Vladimir
1997
A simple proof of the Murasugi and Kauffman theorems on alternating links. Zbl 0668.57009
Turaev, V. G.
1987
Conway and Kauffman modules of a solid torus. Zbl 0706.57004
Turaev, V. G.
1990
Poincaré-Reidemeister metric, Euler structures, and torsion. Zbl 0938.57020
2000
Integrals for braided Hopf algebras. Zbl 0961.16023
Bespalov, Yuri; Kerler, Thomas; Lyubashenko, Volodymyr; Turaev, Vladimir
2000
1992
Crossed group-categories. Zbl 1185.18009
2008
Cobordism of knots on surfaces. Zbl 1166.57008
2008
Semisimple and modular categories from link invariants. Zbl 0888.18001
1997
Double construction for monoidal categories. Zbl 0833.18005
1995
Modular categories and 3-manifold invariants. Zbl 0798.57002
1992
Milnor invariants and Massey products. Zbl 0354.55013
Turaev, V. G.
1976
A combinatorial formulation for the Seiberg-Witten invariants of 3-manifolds. Zbl 1002.57036
1998
On 3-dimensional homotopy quantum field theory. I. Zbl 1254.57012
2012
Monoidal categories and topological field theory. Zbl 1423.18001
2017
Quasi-Poisson structures on representation spaces of surfaces. Zbl 1298.53085
2014
Unoriented topological quantum field theory and link homology. Zbl 1134.57004
2006
Quantum invariants of knots and 3-manifolds. 3rd edition. Zbl 1346.57002
2016
Weyl algebras and knots. Zbl 1123.57006
2007
Knotoids. Zbl 1271.57030
2012
Torsions of $$3$$-manifolds. Zbl 1012.57034
2002
Lectures on topology of words. Zbl 1162.68034
2007
On 3-dimensional homotopy quantum field theory II: the surgery approach. Zbl 1296.57016
2014
Chord diagram invariants of tangles and graphs. Zbl 0947.57010
1998
Biquantization of Lie bialgebras. Zbl 1040.17008
2000
Quantum invariants of links and 3-valent graphs in 3-manifolds. Zbl 0822.57012
1993
Modified $$6j$$-symbols and 3-manifold invariants. Zbl 1237.57011
Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir
2011
Quantum invariants of 3-manifolds and a glimpse of shadow topology. Zbl 0752.57009
1991
Reidemeister torsion and the Alexander polynomial. Zbl 0381.57003
Turaev, V. G.
1978
Intersections of loops in two-dimensional manifolds. Zbl 0422.57005
Turaev, V. G.
1979
A Lagrangian representation of tangles. Zbl 1071.57006
2005
Cohomology ring forms of linking coefficients and invariants of spinor structures in three-dimensional manifolds. Zbl 0519.57009
Turaev, V. G.
1983
Tetrahedral forms in monoidal categories and 3-manifold invariants. Zbl 1261.57013
Geer, Nathan; Kashaev, Rinat; Turaev, Vladimir
2012
The Alexander polynomial of a 3-dimensional manifold. Zbl 0315.57001
Turaev, V. G.
1975
Absolute torsion. Zbl 0934.57030
1999
Quantum groups and ribbon $$G$$-categories. Zbl 1035.57006
2003
Fox pairings and generalized Dehn twists. (Formes de Fox et twists de Dehn généralisés.) Zbl 1297.57005
2013
Dijkgraaf-Witten invariants of surfaces and projective representations of groups. Zbl 1163.57021
2007
Reciprocity for Gauss sums on finite Abelian groups. Zbl 1048.11501
1998
A compactification of the Hurwitz space. Zbl 0929.57001
1999
Cohomology rings, linking forms and invariants of spin structures of three-dimensional manifolds. Zbl 0553.57004
Turaev, V. G.
1984
A norm for the cohomology of 2-complexes. Zbl 1014.57002
2002
Faithful linear representations of the braid groups. Zbl 1050.20026
2002
Formal homotopy quantum field theories. I: Formal maps and crossed $$\mathcal{C}$$-algebras. Zbl 1205.57024
2008
Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0717.57008
Turaev, V. G.
1990
State sum models in low-dimensional topology. Zbl 0744.57007
1991
Curves on surfaces, charts, and words. Zbl 1126.57010
2005
Milnor invariants and Massay products. Zbl 0406.55017
Turaev, V. G.
1979
Knots and words. Zbl 1118.57009
2006
A generalization of several classical invariants of links. Zbl 1148.57005
2007
On reciprocity. Zbl 1167.11030
2007
Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0693.57013
Turaev, V. G.
1989
A cocycle for the symplectic first Chern class and Maslov indices. Zbl 0556.55012
Turaev, V. G.
1984
2013
A semigroup of theta-curves in 3-manifolds. Zbl 1284.57012
2011
On the definition of the 2-category of 2-knots. Zbl 0851.18003
Kharlamov, V. M.; Turaev, V. G.
1996
A function on the homology of 3-manifolds. Zbl 1145.57011
2007
A cocycle for the symplectic first Chern class and the Maslov index. Zbl 0577.55011
Turaev, V. G.
1984
First symplectic Chern class and Maslov indices. Zbl 0612.55019
Turaev, V. G.
1987
On certain enumeration problems in two-dimensional topology. Zbl 1175.57013
2009
Poisson-Gerstenhaber brackets in representation algebras. Zbl 1308.17027
2014
Quantum invariants of 3-manifold and a glimpse of shadow topology. Zbl 0752.57010
1992
Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024
Frenkel, Igor B.; Turaev, Vladimir G.
1995
Cobordisms of words. Zbl 1221.57032
2008
The first symplectic Chern class and the Maslov indices. Zbl 0577.55012
Turaev, V. G.
1985
Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0853.57016
Turaev, V. G.
1994
A canonical cocycle for the Euler class of a flat vector bundle. Zbl 0518.57012
Ivanov, V. N.; Turaev, V. G.
1982
Intersections of loops in two-dimensional manifolds. II: Free loops. Zbl 0543.57007
Turaev, V. G.; Viro, O. Ya.
1984
The Alexander polynomial of a three-dimensional manifold. Zbl 0339.57002
Turaev, V. G.
1976
Complexity of virtual 3-manifolds. Zbl 1362.57028
Vesnin, Andrei Yu.; Turaev, Vladimir G.; Fominykh, Evgeny A.
2016
Dijkgraaf-Witten invariants over $$\mathbb Z_2$$ for 3-manifolds. Zbl 1327.57019
Matveev, S. V.; Turaev, V. G.
2015
Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0732.57008
Turaev, V. G.
1989
Schnitte von Schleifen in zweidimensionalen Mannigfaltigkeiten. Zbl 0384.57004
Turaev, V. G.
1978
Loops on surfaces, Feynman diagrams, and trees. Zbl 1094.57022
2005
A Lagrangian representation of tangles. II. Zbl 1106.57004
2006
Nilpotent homotopy types of closed 3-manifolds. Zbl 0564.57008
Turaev, V. G.
1984
The Conway and Kauffman modules of the solid torus. Zbl 0928.57014
1997
Higher skein modules. Zbl 0991.57015
1999
Kuperberg and Turaev-Viro invariants in unimodular categories. Zbl 1454.18014
Costantino, Francesco; Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir
2020
Trimming of metric spaces and the tight span. Zbl 1402.54029
2018
Monoidal categories and topological field theory. Zbl 1423.18001
2017
Brackets in the Pontryagin algebras of manifolds. (Crochets dans les algèbres de Pontryagin des variétés.) Zbl 1416.17012
2017
Quantum invariants of knots and 3-manifolds. 3rd edition. Zbl 1346.57002
2016
Complexity of virtual 3-manifolds. Zbl 1362.57028
Vesnin, Andrei Yu.; Turaev, Vladimir G.; Fominykh, Evgeny A.
2016
Dijkgraaf-Witten invariants over $$\mathbb Z_2$$ for 3-manifolds. Zbl 1327.57019
Matveev, S. V.; Turaev, V. G.
2015
Three-dimensional manifolds with poor spines. Zbl 1328.57026
Vesnin, A. Yu.; Turaev, V. G.; Fominykh, E. A.
2015
Quasi-Poisson structures on representation spaces of surfaces. Zbl 1298.53085
2014
On 3-dimensional homotopy quantum field theory II: the surgery approach. Zbl 1296.57016
2014
Poisson-Gerstenhaber brackets in representation algebras. Zbl 1308.17027
2014
Fox pairings and generalized Dehn twists. (Formes de Fox et twists de Dehn généralisés.) Zbl 1297.57005
2013
2013
Marked fatgraph complexes and surface automorphisms. Zbl 1367.57012
Kuno, Yusuke; Penner, R. C.; Turaev, Vladimir
2013
On 3-dimensional homotopy quantum field theory. I. Zbl 1254.57012
2012
Knotoids. Zbl 1271.57030
2012
Tetrahedral forms in monoidal categories and 3-manifold invariants. Zbl 1261.57013
Geer, Nathan; Kashaev, Rinat; Turaev, Vladimir
2012
Modified $$6j$$-symbols and 3-manifold invariants. Zbl 1237.57011
Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir
2011
A semigroup of theta-curves in 3-manifolds. Zbl 1284.57012
2011
Quantum invariants of knots and 3-manifolds. 2nd revised ed. Zbl 1213.57002
2010
Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier. Zbl 1243.81016
2010
Remarks on 2-dimensional HQFTs. Zbl 1226.57043
2010
Enumeration of lifts of commuting elements of a group. Zbl 1214.20012
2010
Modified quantum dimensions and re-normalized link invariants. Zbl 1160.81022
Geer, Nathan; Patureau-Mirand, Bertrand; Turaev, Vladimir
2009
On certain enumeration problems in two-dimensional topology. Zbl 1175.57013
2009
Braid groups. With the graphical assistance of Olivier Dodane. Zbl 1208.20041
2008
Crossed group-categories. Zbl 1185.18009
2008
Cobordism of knots on surfaces. Zbl 1166.57008
2008
Formal homotopy quantum field theories. I: Formal maps and crossed $$\mathcal{C}$$-algebras. Zbl 1205.57024
2008
Cobordisms of words. Zbl 1221.57032
2008
Topology of words. Zbl 1145.57018
2007
Weyl algebras and knots. Zbl 1123.57006
2007
Lectures on topology of words. Zbl 1162.68034
2007
Dijkgraaf-Witten invariants of surfaces and projective representations of groups. Zbl 1163.57021
2007
A generalization of several classical invariants of links. Zbl 1148.57005
2007
On reciprocity. Zbl 1167.11030
2007
A function on the homology of 3-manifolds. Zbl 1145.57011
2007
Coalgebras of words and phrases. Zbl 1136.16037
2007
Unoriented topological quantum field theory and link homology. Zbl 1134.57004
2006
Knots and words. Zbl 1118.57009
2006
A Lagrangian representation of tangles. II. Zbl 1106.57004
2006
A Lagrangian representation of tangles. Zbl 1071.57006
2005
Curves on surfaces, charts, and words. Zbl 1126.57010
2005
Loops on surfaces, Feynman diagrams, and trees. Zbl 1094.57022
2005
Knot theory for self-indexed graphs. Zbl 1074.57005
2005
Virtual strings. Zbl 1066.57022
2004
Invariants of knots and 3-manifolds from quantum groupoids. Zbl 1021.16026
Nikshych, Dmitri; Turaev, Vladimir; Vainerman, Leonid
2003
Quantum groups and ribbon $$G$$-categories. Zbl 1035.57006
2003
Torsions of 3-dimensional manifolds. Zbl 1012.57002
Turaev, V.
2002
Torsions of $$3$$-manifolds. Zbl 1012.57034
2002
A norm for the cohomology of 2-complexes. Zbl 1014.57002
2002
Faithful linear representations of the braid groups. Zbl 1050.20026
2002
Invariants of knots and 3-manifolds. Proceedings of the workshop, Kyoto, Japan, September 17–21, 2001. Zbl 0996.00037
Ohtsuki, T.; Kohno, T.; Le, T.; Murakami, J.; Roberts, J.; Turaev, V.
2002
Introduction to combinatorial torsions. Notes taken by Felix Schlenk. Zbl 0970.57001
Turaev, V. G.
2001
Higher skein modules. II. Zbl 1008.57011
2001
Poincaré-Reidemeister metric, Euler structures, and torsion. Zbl 0938.57020
2000
Integrals for braided Hopf algebras. Zbl 0961.16023
Bespalov, Yuri; Kerler, Thomas; Lyubashenko, Volodymyr; Turaev, Vladimir
2000
Biquantization of Lie bialgebras. Zbl 1040.17008
2000
Counting lattice points of rational polyhedra. Zbl 0988.52020
2000
Absolute torsion. Zbl 0934.57030
1999
A compactification of the Hurwitz space. Zbl 0929.57001
1999
Higher skein modules. Zbl 0991.57015
1999
A combinatorial formulation for the Seiberg-Witten invariants of 3-manifolds. Zbl 1002.57036
1998
Chord diagram invariants of tangles and graphs. Zbl 0947.57010
1998
Reciprocity for Gauss sums on finite Abelian groups. Zbl 1048.11501
1998
Systems of correlators and solutions of the WDVV equations. Zbl 0906.35098
1998
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016
Frenkel, Igor B.; Turaev, Vladimir G.
1997
Torsion invariants of Spin$$^c$$-structures on 3-manifolds. Zbl 0891.57019
1997
Quantum groups and knot invariants. Zbl 0878.17013
Kassel, Christian; Rosso, Marc; Turaev, Vladimir
1997
Semisimple and modular categories from link invariants. Zbl 0888.18001
1997
The Conway and Kauffman modules of the solid torus. Zbl 0928.57014
1997
On the definition of the 2-category of 2-knots. Zbl 0851.18003
Kharlamov, V. M.; Turaev, V. G.
1996
Double construction for monoidal categories. Zbl 0833.18005
1995
Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024
Frenkel, Igor B.; Turaev, Vladimir G.
1995
Quantum invariants of knots and 3-manifolds. Zbl 0812.57003
Turaev, V. G.
1994
Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0853.57016
Turaev, V. G.
1994
Quantum invariants of 3-manifolds associated with classical simple Lie algebras. Zbl 0784.57007
Turaev, V.; Wenzl, H.
1993
Quantum invariants of links and 3-valent graphs in 3-manifolds. Zbl 0822.57012
1993
State sum invariants of 3-manifolds and quantum $$6j$$-symbols. Zbl 0779.57009
Turaev, V. G.; Viro, O. Y.
1992
1992
Modular categories and 3-manifold invariants. Zbl 0798.57002
1992
Quantum invariants of 3-manifold and a glimpse of shadow topology. Zbl 0752.57010
1992
Invariants of 3-manifolds via link polynomials and quantum groups. Zbl 0725.57007
Reshetikhin, N.; Turaev, V. G.
1991
Skein quantization of Poisson algebras of loops on surfaces. Zbl 0758.57011
1991
Quantum invariants of 3-manifolds and a glimpse of shadow topology. Zbl 0752.57009
1991
State sum models in low-dimensional topology. Zbl 0744.57007
1991
Ribbon graphs and their invariants derived from quantum groups. Zbl 0768.57003
Reshetikhin, N. Yu.; Turaev, V. G.
1990
Euler structures, nonsingular vector fields, and torsions of Reidemeister type. Zbl 0692.57015
Turaev, V. G.
1990
Operator invariants of tangles, and R-matrices. Zbl 0707.57003
Turaev, V. G.
1990
Conway and Kauffman modules of a solid torus. Zbl 0706.57004
Turaev, V. G.
1990
Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0717.57008
Turaev, V. G.
1990
Jones-type invariants of tangles. Zbl 0706.57005
Turaev, V. G.
1990
Three-dimensional Poincaré complexes: Homotopy classification and splitting. Zbl 0693.57013
Turaev, V. G.
1989
Algebras of loops on surfaces, algebras of knots, and quantization. Zbl 0732.57008
Turaev, V. G.
1989
Category of oriented tangles and its representations. Zbl 0705.57008
Turaev, V. G.
1989
The Yang-Baxter equation and invariants of links. Zbl 0648.57003
Turaev, V. G.
1988
The Conway and Kauffman modules of the solid torus. Zbl 0673.57004
Turaev, V. G.
1988
Homeomorphisms of three-dimensional geometric manifolds. Zbl 0646.57008
Turaev, V. G.
1988
Classification of oriented Montesinos links via spin structures. Zbl 0648.57002
Turaev, V. G.
1988
Towards the topological classification of geometric 3-manifolds. Zbl 0651.57011
Turaev, V. G.
1988
...and 27 more Documents
all top 5

#### Cited by 1,688 Authors

 43 Turaev, Vladimir G. 32 Kauffman, Louis Hirsch 27 Le, Thang Tu Quoc 26 Garoufalidis, Stavros 24 Morozov, Alexei Yurievich 24 Runkel, Ingo 24 Wang, Shuanhong 23 Wang, Zhenghan 22 Schweigert, Christoph 21 Geer, Nathan 20 Rowell, Eric C. 19 Mironov, Andrei D. 18 Patureau-Mirand, Bertrand 16 Friedl, Stefan 16 Fuchs, Jürgen 15 Andersen, Jørgen Ellegaard 14 Manturov, Vassiliĭ Olegovich 13 Gilmer, Patrick M. 13 Reshetikhin, Nikolai Yu. 12 Costantino, Francesco 12 Kong, Liang 12 Murakami, Jun 11 Dittrich, Bianca 11 Hikami, Kazuhiro 11 Kadokami, Teruhisa 11 Morozov, Andreĭ Alekseevich 10 Lambropoulou, Sofia S. F. 10 Massuyeau, Gwénaël 10 Rozansky, Lev 10 Virelizier, Alexis 10 Xu, Feng 9 Beliakova, Anna 9 Freedman, Michael Hartley 9 Kashaev, Rinat M. 9 Mroczkowski, Maciej 9 Przytycki, Józef H. 9 Ramadevi, Pichai 9 Schlosser, Michael J. 9 Thuillier, Frank 9 Wenzl, Hans 9 Zhang, Ruibin 8 Baez, John C. 8 Gainutdinov, Azat M. 8 Gould, Mark D. 8 Majid, Shahn 8 Masbaum, Gregor 8 Matveev, Sergeĭ Vladimirovich 8 Nikshych, Dmitri 8 Rosengren, Hjalmar 8 Saito, Masahico 8 Spiridonov, Vyacheslav Pavlovich 8 Takata, Toshie 8 Wong, Helen M. 7 Alonso Álvarez, José Nicanor 7 Barrett, John William 7 Blanchet, Christian 7 Bruguières, Alain 7 Carter, J. Scott 7 Chrisman, Micah Whitney 7 Freidel, Laurent 7 Frohman, Charles D. 7 Gabrovšek, Boštjan 7 Gavarini, Fabio 7 González Rodríguez, Ramón 7 Hahn, Atle 7 Im, Young Ho 7 Kuno, Yusuke 7 Livine, Etera R. 7 Marché, Julien 7 Marzuoli, Annalisa 7 Ohtsuki, Tomotada 7 Petronio, Carlo 7 Riello, Aldo 7 Shimizu, Kenichi 7 Snyder, Noah 7 Tarkaev, Vladimir Viktorovich 6 Alekseev, Anton Yu. 6 Benedetti, Riccardo 6 Bonahon, Francis 6 Davydov, Alekseĭ Aleksandrovich 6 Delcamp, Clement 6 Dubois, Jérôme 6 Fernández Vilaboa, José Manuel 6 Frenkel, Igor B. 6 Galindo Martínez, César Neyit 6 Gelca, Răzvan 6 Gukov, Sergei 6 Habiro, Kazuo 6 Hajij, Mustafa 6 Hillman, Jonathan Arthur 6 Jaeger, François 6 Kania-Bartoszyńska, Joanna 6 Khovanov, Mikhail G. 6 Kitayama, Takahiro 6 Koda, Yuya 6 Korepanov, Igor Germanovich 6 Lawrence, Ruth J. 6 Lin, Xiao-Song 6 Morton, Hugh R. 6 Murakami, Hitoshi ...and 1,588 more Authors
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#### Cited in 235 Serials

 202 Journal of Knot Theory and its Ramifications 155 Communications in Mathematical Physics 96 Algebraic & Geometric Topology 84 Journal of Mathematical Physics 78 Advances in Mathematics 69 Journal of Algebra 62 Journal of High Energy Physics 57 Transactions of the American Mathematical Society 55 Topology and its Applications 46 Journal of Pure and Applied Algebra 45 Journal of Geometry and Physics 42 Geometry & Topology 34 Letters in Mathematical Physics 33 Communications in Algebra 33 Nuclear Physics. B 31 Proceedings of the American Mathematical Society 22 Mathematical Proceedings of the Cambridge Philosophical Society 20 Duke Mathematical Journal 20 Mathematische Annalen 20 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 20 Quantum Topology 19 Selecta Mathematica. New Series 17 Theoretical and Mathematical Physics 17 International Journal of Mathematics 16 Communications in Contemporary Mathematics 15 Annales de l’Institut Fourier 15 Algebras and Representation Theory 14 Geometriae Dedicata 14 Inventiones Mathematicae 13 Bulletin of the American Mathematical Society. New Series 13 Applied Categorical Structures 13 Journal of Mathematical Sciences (New York) 13 Annales Henri Poincaré 12 Mathematische Zeitschrift 11 International Journal of Modern Physics A 11 Journal of Algebra and its Applications 10 Israel Journal of Mathematics 10 Journal of the American Mathematical Society 10 Annals of Physics 10 The Ramanujan Journal 9 Compositio Mathematica 9 Manuscripta Mathematica 8 Reviews in Mathematical Physics 8 Acta Mathematica Vietnamica 8 Osaka Journal of Mathematics 8 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Theory and Applications of Categories 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Journal of Topology 7 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 7 Experimental Mathematics 7 St. Petersburg Mathematical Journal 7 Proceedings of the Steklov Institute of Mathematics 6 Discrete Mathematics 6 General Relativity and Gravitation 6 Fundamenta Mathematicae 6 Journal of Combinatorial Theory. Series A 6 European Journal of Combinatorics 6 Journal of Algebraic Combinatorics 6 Science China. Mathematics 5 Bulletin of the Australian Mathematical Society 5 Classical and Quantum Gravity 5 Journal of Soviet Mathematics 5 Transformation Groups 5 Acta Mathematica Sinica. English Series 5 International Journal of Geometric Methods in Modern Physics 5 Mediterranean Journal of Mathematics 4 Modern Physics Letters A 4 Mathematical Notes 4 Physics Letters. B 4 Chaos, Solitons and Fractals 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Journal of Combinatorial Theory. Series B 4 Memoirs of the American Mathematical Society 4 Proceedings of the Japan Academy. Series A 4 Siberian Mathematical Journal 4 Tohoku Mathematical Journal. Second Series 4 Tokyo Journal of Mathematics 4 Advances in Applied Mathematics 4 Linear Algebra and its Applications 4 Indagationes Mathematicae. New Series 4 Boletín de la Sociedad Matemática Mexicana. Third Series 4 Living Reviews in Relativity 4 Quantum Information Processing 4 Journal of Noncommutative Geometry 4 Journal of Physics A: Mathematical and Theoretical 4 Winter Braids Lecture Notes 3 Rocky Mountain Journal of Mathematics 3 Russian Mathematical Surveys 3 Acta Mathematica 3 Glasgow Mathematical Journal 3 Publications Mathématiques 3 Journal für die Reine und Angewandte Mathematik 3 Pacific Journal of Mathematics 3 Constructive Approximation 3 Discrete & Computational Geometry 3 Expositiones Mathematicae 3 Chinese Science Bulletin 3 Annales Mathématiques Blaise Pascal 3 Doklady Mathematics ...and 135 more Serials
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#### Cited in 53 Fields

 1,118 Manifolds and cell complexes (57-XX) 609 Quantum theory (81-XX) 360 Nonassociative rings and algebras (17-XX) 343 Associative rings and algebras (16-XX) 320 Category theory; homological algebra (18-XX) 225 Group theory and generalizations (20-XX) 144 Global analysis, analysis on manifolds (58-XX) 123 Differential geometry (53-XX) 98 Relativity and gravitational theory (83-XX) 89 Combinatorics (05-XX) 89 Algebraic geometry (14-XX) 77 Functional analysis (46-XX) 69 Special functions (33-XX) 59 Number theory (11-XX) 58 Algebraic topology (55-XX) 53 Statistical mechanics, structure of matter (82-XX) 41 Topological groups, Lie groups (22-XX) 36 Dynamical systems and ergodic theory (37-XX) 32 Several complex variables and analytic spaces (32-XX) 30 Computer science (68-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 20 $$K$$-theory (19-XX) 16 Functions of a complex variable (30-XX) 14 Commutative algebra (13-XX) 13 Information and communication theory, circuits (94-XX) 12 Probability theory and stochastic processes (60-XX) 10 Convex and discrete geometry (52-XX) 9 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 8 Partial differential equations (35-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 General topology (54-XX) 6 Difference and functional equations (39-XX) 6 Abstract harmonic analysis (43-XX) 5 Mathematical logic and foundations (03-XX) 5 Field theory and polynomials (12-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Operator theory (47-XX) 5 Geometry (51-XX) 4 Numerical analysis (65-XX) 4 Mechanics of particles and systems (70-XX) 3 Approximations and expansions (41-XX) 3 Statistics (62-XX) 3 Operations research, mathematical programming (90-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 General algebraic systems (08-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-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)

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