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## Kohno, Toshitake

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 Author ID: kohno.toshitake Published as: Kohno, Toshitake; Kohno, T.
 Documents Indexed: 59 Publications since 1983, including 11 Books
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#### Co-Authors

 46 single-authored 2 Funar, Louis 2 Pajitnov, Andrei Vladimirovich 2 Takata, Toshie 1 Carter, J. Scott 1 Cohen, Frederick Ronald 1 Fukaya, Kenji 1 Furuta, Mikio 1 Iwase, Norio 1 Kamada, Seiichi 1 Kauffman, Louis Hirsch 1 Kawauchi, Akio 1 Kotschick, Dieter 1 Le, Thang Tu Quoc 1 Levi, Ran 1 Morishita, Masanori 1 Murakami, Jun 1 Oda, Takayuki 1 Ohtsuki, Tomotada 1 Tamaki, Dai 1 Turaev, Vladimir G. 1 Wu, Jie 1 Xicoténcatl, Miguel A.
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#### Serials

 3 Topology and its Applications 3 Sūgaku 2 Proceedings of the Japan Academy. Series A 2 Forum Mathematicum 2 Sugaku Expositions 2 Journal of Knot Theory and its Ramifications 2 RIMS Kokyuroku 2 Geometry and Topology Monographs 1 International Journal of Modern Physics B 1 Acta Mathematica Vietnamica 1 Annales de l’Institut Fourier 1 Geometriae Dedicata 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Pure and Applied Algebra 1 Nagoya Mathematical Journal 1 European Mathematical Society Newsletter 1 Central European Journal of Mathematics 1 Advanced Series in Mathematical Physics 1 Contemporary Mathematics 1 Series on Knots and Everything 1 Translations of Mathematical Monographs 1 Journal of Singularities 1 European Journal of Mathematics
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#### Fields

 43 Manifolds and cell complexes (57-XX) 28 Group theory and generalizations (20-XX) 16 Nonassociative rings and algebras (17-XX) 15 Algebraic topology (55-XX) 13 Quantum theory (81-XX) 11 Several complex variables and analytic spaces (32-XX) 9 General and overarching topics; collections (00-XX) 9 Algebraic geometry (14-XX) 9 Differential geometry (53-XX) 8 Global analysis, analysis on manifolds (58-XX) 4 Special functions (33-XX) 4 Convex and discrete geometry (52-XX) 2 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

41 Publications have been cited 324 times in 250 Documents Cited by Year
Monodromy representations of braid groups and Yang-Baxter equations. Zbl 0634.58040
Kohno, Toshitake
1987
Série de Poincaré-Koszul associée aux groupes de tresses pures. Zbl 0574.55009
Kohno, Toshitake
1985
On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces. Zbl 0503.57001
Kohno, Toshitake
1983
Homology of a local system on the complement of hyperplanes. Zbl 0611.55005
Kohno, Toshitake
1986
Linear representations of braid groups and classical Yang-Baxter equations. Zbl 0661.20026
Kohno, Toshitake
1988
Vassiliev invariants and de Rham complex on the space of knots. Zbl 0876.57009
Kohno, Toshitake
1994
On Burau’s representations at roots of unity. Zbl 1298.57002
Funar, Louis; Kohno, Toshitake
2014
Conformal field theory and topology. Transl. from the Japanese by the author. Zbl 1024.81001
Kohno, Toshitake
2002
Quantum and homological representations of braid groups. Zbl 1284.32020
Kohno, Toshitake
2012
Integrable connections related to Manin and Schechtman’s higher braid groups. Zbl 0748.57008
Kohno, Toshitake
1990
Vassiliev invariants of braids and iterated integrals. Zbl 0978.57006
Kohno, Toshitake
2000
Symmetry of Witten’s 3-manifold invariants for sl$$(n,\mathbb{C})$$. Zbl 0795.57004
Kohno, Toshitake; Takata, Toshie
1993
Loop spaces of configuration spaces and finite type invariants. Zbl 1043.57004
Kohno, Toshitake
2002
Orbit configuration spaces associated to discrete subgroups of $$\mathrm{PSL}(2,\mathbb R)$$. Zbl 1196.55022
Cohen, F. R.; Kohno, Toshitake; Xicoténcatl, M. A.
2009
Novikov homology, jump loci and Massey products. Zbl 1308.55003
Kohno, Toshitake; Pajitnov, Andrei
2014
The lower central series of the pure braid group of an algebraic curve. Zbl 0642.20035
Kohno, Toshitake; Oda, Takayuki
1987
Elliptic KZ system, braid group of the torus and Vassiliev invariants. Zbl 0878.57008
Kohno, Toshitake
1997
Level-rank duality of Witten’s 3-manifold invariants. Zbl 0860.57013
Kohno, Toshitake; Takata, Toshie
1996
Homological representations of braid groups and KZ connections. Zbl 1292.32019
Kohno, Toshitake
2012
Circle-valued Morse theory for complex hyperplane arrangements. Zbl 1336.14036
Kohno, Toshitake; Pajitnov, Andrei
2015
Free subgroups within the images of quantum representations. Zbl 1303.57002
Funar, Louis; Kohno, Toshitake
2014
Geometry of iterated integrals. (Hanpuku sekibun no kikagaku). Zbl 1305.26004
Kohno, Toshitake
2009
Hecke algebra representations of braid groups and classical Yang-Baxter equations. Zbl 0667.17009
Kohno, Toshitake
1988
Differential forms and the fundamental group of the complement of hypersurfaces. Zbl 0519.57001
Kohno, Toshitake
1983
Three-manifold invariants derived from conformal field theory and projective representations of modular groups. Zbl 0821.57012
Kohno, Toshitake
1992
Tunnel numbers of knots and Jones-Witten invariants. Zbl 0851.57005
Kohno, Toshitake
1994
Bar complex of the Orlik-Solomon algebra. Zbl 0995.32018
Kohno, Toshitake
2002
An algebraic computation of the Alexander polynomial of a plane algebraic curve. Zbl 0524.14028
Kohno, Toshitake
1983
Bar complex, configuration spaces and finite type invariants for braids. Zbl 1181.57016
Kohno, Toshitake
2010
Higher holonomy of formal homology connections and braid cobordisms. Zbl 1398.57017
Kohno, Toshitake
2016
Topological invariants for 3-manifolds using representations of mapping class groups. II: Estimating tunnel number of knots. Zbl 0823.57004
Kohno, Toshitake
1994
Primes and knots. Proceedings of an AMS special session, Baltimore, MD, USA, January 15–16, 2003 and the 15th JAMI (Japan-US Mathematics Institute) conference, Baltimore, MD, USA, March 7–16, 2003. Zbl 1102.11001
Kohno, Toshitake (ed.); Morishita, Masanori (ed.)
2006
Hyperplane arrangements, local system homology and iterated integrals. Zbl 1261.20037
Kohno, Toshitake
2012
Invariants of knots and 3-manifolds. Proceedings of the workshop, Kyoto, Japan, September 17–21, 2001. Zbl 0996.00037
Ohtsuki, T. (ed.); Kohno, T. (ed.); Le, T. (ed.); Murakami, J. (ed.); Roberts, J. (ed.); Turaev, V. (ed.)
2002
Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups. Zbl 0674.57003
Kohno, Toshitake
1989
New developments in the theory of knots. Zbl 0727.57001
Kohno, Toshitake (ed.)
1990
Invariants of 3-manifolds based on conformal field theory and Heegaard splitting. Zbl 0752.57008
Kohno, Toshitake
1992
Integrable systems related to braid groups and Yang-Baxter equation. Zbl 0716.17012
Kohno, Toshitake
1989
Topological quantum field theory – centered around its applications to 3-dimensional manifolds. Zbl 0759.57008
Kohno, Toshitake
1992
The volume of a hyperbolic simplex and iterated integrals. Zbl 1139.51001
Kohno, Toshitake
2007
Local systems on configuration spaces, KZ connections and conformal blocks. Zbl 1311.52017
Kohno, Toshitake
2014
Higher holonomy of formal homology connections and braid cobordisms. Zbl 1398.57017
Kohno, Toshitake
2016
Circle-valued Morse theory for complex hyperplane arrangements. Zbl 1336.14036
Kohno, Toshitake; Pajitnov, Andrei
2015
On Burau’s representations at roots of unity. Zbl 1298.57002
Funar, Louis; Kohno, Toshitake
2014
Novikov homology, jump loci and Massey products. Zbl 1308.55003
Kohno, Toshitake; Pajitnov, Andrei
2014
Free subgroups within the images of quantum representations. Zbl 1303.57002
Funar, Louis; Kohno, Toshitake
2014
Local systems on configuration spaces, KZ connections and conformal blocks. Zbl 1311.52017
Kohno, Toshitake
2014
Quantum and homological representations of braid groups. Zbl 1284.32020
Kohno, Toshitake
2012
Homological representations of braid groups and KZ connections. Zbl 1292.32019
Kohno, Toshitake
2012
Hyperplane arrangements, local system homology and iterated integrals. Zbl 1261.20037
Kohno, Toshitake
2012
Bar complex, configuration spaces and finite type invariants for braids. Zbl 1181.57016
Kohno, Toshitake
2010
Orbit configuration spaces associated to discrete subgroups of $$\mathrm{PSL}(2,\mathbb R)$$. Zbl 1196.55022
Cohen, F. R.; Kohno, Toshitake; Xicoténcatl, M. A.
2009
Geometry of iterated integrals. (Hanpuku sekibun no kikagaku). Zbl 1305.26004
Kohno, Toshitake
2009
The volume of a hyperbolic simplex and iterated integrals. Zbl 1139.51001
Kohno, Toshitake
2007
Primes and knots. Proceedings of an AMS special session, Baltimore, MD, USA, January 15–16, 2003 and the 15th JAMI (Japan-US Mathematics Institute) conference, Baltimore, MD, USA, March 7–16, 2003. Zbl 1102.11001
Kohno, Toshitake; Morishita, Masanori
2006
Conformal field theory and topology. Transl. from the Japanese by the author. Zbl 1024.81001
Kohno, Toshitake
2002
Loop spaces of configuration spaces and finite type invariants. Zbl 1043.57004
Kohno, Toshitake
2002
Bar complex of the Orlik-Solomon algebra. Zbl 0995.32018
Kohno, Toshitake
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
Vassiliev invariants of braids and iterated integrals. Zbl 0978.57006
Kohno, Toshitake
2000
Elliptic KZ system, braid group of the torus and Vassiliev invariants. Zbl 0878.57008
Kohno, Toshitake
1997
Level-rank duality of Witten’s 3-manifold invariants. Zbl 0860.57013
Kohno, Toshitake; Takata, Toshie
1996
Vassiliev invariants and de Rham complex on the space of knots. Zbl 0876.57009
Kohno, Toshitake
1994
Tunnel numbers of knots and Jones-Witten invariants. Zbl 0851.57005
Kohno, Toshitake
1994
Topological invariants for 3-manifolds using representations of mapping class groups. II: Estimating tunnel number of knots. Zbl 0823.57004
Kohno, Toshitake
1994
Symmetry of Witten’s 3-manifold invariants for sl$$(n,\mathbb{C})$$. Zbl 0795.57004
Kohno, Toshitake; Takata, Toshie
1993
Three-manifold invariants derived from conformal field theory and projective representations of modular groups. Zbl 0821.57012
Kohno, Toshitake
1992
Invariants of 3-manifolds based on conformal field theory and Heegaard splitting. Zbl 0752.57008
Kohno, Toshitake
1992
Topological quantum field theory – centered around its applications to 3-dimensional manifolds. Zbl 0759.57008
Kohno, Toshitake
1992
Integrable connections related to Manin and Schechtman’s higher braid groups. Zbl 0748.57008
Kohno, Toshitake
1990
New developments in the theory of knots. Zbl 0727.57001
Kohno, Toshitake
1990
Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups. Zbl 0674.57003
Kohno, Toshitake
1989
Integrable systems related to braid groups and Yang-Baxter equation. Zbl 0716.17012
Kohno, Toshitake
1989
Linear representations of braid groups and classical Yang-Baxter equations. Zbl 0661.20026
Kohno, Toshitake
1988
Hecke algebra representations of braid groups and classical Yang-Baxter equations. Zbl 0667.17009
Kohno, Toshitake
1988
Monodromy representations of braid groups and Yang-Baxter equations. Zbl 0634.58040
Kohno, Toshitake
1987
The lower central series of the pure braid group of an algebraic curve. Zbl 0642.20035
Kohno, Toshitake; Oda, Takayuki
1987
Homology of a local system on the complement of hyperplanes. Zbl 0611.55005
Kohno, Toshitake
1986
Série de Poincaré-Koszul associée aux groupes de tresses pures. Zbl 0574.55009
Kohno, Toshitake
1985
On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces. Zbl 0503.57001
Kohno, Toshitake
1983
Differential forms and the fundamental group of the complement of hypersurfaces. Zbl 0519.57001
Kohno, Toshitake
1983
An algebraic computation of the Alexander polynomial of a plane algebraic curve. Zbl 0524.14028
Kohno, Toshitake
1983
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#### Cited by 249 Authors

 16 Suciu, Alexander I. 11 Kohno, Toshitake 8 Leksin, Vladimir Pavlovich 6 Cohen, Frederick Ronald 6 Hain, Richard M. 6 Papadima, Ștefan 5 Felder, Giovanni 5 Funar, Louis 5 Marin, Ivan 5 Varchenko, Alexander Nikolaevich 5 Wang, He 5 Yoshinaga, Masahiko 4 Denham, Graham 4 Guaschi, John 4 Ito, Tetsuya 4 Le, Thang Tu Quoc 4 Pajitnov, Andrei Vladimirovich 3 Abe, Yasuhiro 3 Dimca, Alexandru 3 Etingof, Pavel Il’ich 3 Falk, Michael J. 3 Gawȩdzki, Krzysztof 3 Golubeva, Valentina Alekseevna 3 Gonçalves, Daciberg Lima 3 Salvetti, Mario 3 Settepanella, Simona 3 Terao, Hiroaki 3 Wu, Jie 3 Yuzvinsky, Sergey 2 Arsie, Alessandro 2 Asada, Mamoru 2 Birman, Joan S. 2 Brendle, Tara E. 2 Brochier, Adrien 2 Church, Thomas 2 Cirio, Lucio Simone 2 Cohen, Daniel C. 2 Enriquez, Benjamin 2 Farb, Benson 2 Fröhlich, Jürg Martin 2 Gaiffi, Giovanni 2 Gitler Hammer, Samuel Carlos 2 Haraoka, Yoshishige 2 Jambu, Michel 2 Kawahara, Yukihito 2 Kirin, N. A. 2 Komendarczyk, Rafal 2 Lawrence, Ruth J. 2 Lorenzoni, Paolo 2 Maakestad, Helge Øystein 2 Margalit, Dan 2 Martins, João Nuno Goncalves Faria 2 Matsuo, Atsushi 2 Murakami, Jun 2 Ocampo Uribe, Oscar Eduardo 2 Oh, Phillial 2 Orlik, Peter 2 Paris, Luis 2 Rains, Eric M. 2 Reshetikhin, Nikolai Yu. 2 Sato, Nobuya 2 Silvotti, Roberto 2 Stylianakis, Charalampos 2 Tarasov, Vitaly Olegovich 2 Toledano Laredo, Valerio 2 Vershinin, Vladimir V. 2 Xicoténcatl, Miguel A. 1 Aguirre, Leonardo 1 Andersen, Jørgen Ellegaard 1 Aomoto, Kazuhiko 1 Babichenko, Andrei 1 Bahri, Anthony P. 1 Bailet, Pauline 1 Bannai, Eiichi 1 Bardakov, Valeriĭ Georgievich 1 Bartholdi, Laurent 1 Baseilhac, Stéphane 1 Bellingeri, Paolo 1 Bendersky, Martin 1 Benedetti, Riccardo 1 Berceanu, Barbu Rudolf 1 Berrick, A. Jon 1 Bezrukavnikov, Roman 1 Blanchet, Christian 1 Budney, Ryan David 1 Buffenoir, E. 1 Buhot, Arnaud 1 Calaque, Damien 1 Chen, Junda 1 Chen, Yuqun 1 Chen, Zhi 1 Cogolludo Agustín, José Ignacio 1 Cohen, Fred R. 1 Conner, Andrew 1 Coulon, Rémi B. 1 Davis, Michael W. 1 De Concini, Corrado 1 de Jong, Aise Johan 1 de Miranda e Pereiro, Carolina 1 Degiovanni, Pascal ...and 149 more Authors
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#### Cited in 90 Serials

 29 Communications in Mathematical Physics 14 Topology and its Applications 11 Inventiones Mathematicae 11 Journal of Algebra 9 Annales de l’Institut Fourier 9 Transactions of the American Mathematical Society 8 Advances in Mathematics 7 Journal of Pure and Applied Algebra 7 Geometry & Topology 6 Journal of Knot Theory and its Ramifications 6 Journal of Mathematical Sciences (New York) 6 Selecta Mathematica. New Series 5 Duke Mathematical Journal 5 European Journal of Mathematics 4 Communications in Algebra 4 Journal of Mathematical Physics 4 Letters in Mathematical Physics 4 Mathematische Zeitschrift 4 Journal of the American Mathematical Society 4 Algebraic & Geometric Topology 3 Israel Journal of Mathematics 3 Nuclear Physics. B 3 Compositio Mathematica 3 Functional Analysis and its Applications 3 Proceedings of the American Mathematical Society 3 Proceedings of the Steklov Institute of Mathematics 2 Mathematical Notes 2 Acta Mathematica Vietnamica 2 Mathematische Annalen 2 Proceedings of the Japan Academy. Series A 2 International Journal of Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Dynamical and Control Systems 2 Journal of High Energy Physics 2 Journal of Singularities 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Russian Mathematical Surveys 1 Theoretical and Mathematical Physics 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Algebra and Logic 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Kodai Mathematical Journal 1 Mathematische Nachrichten 1 Nagoya Mathematical Journal 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Siberian Mathematical Journal 1 Transactions of the Moscow Mathematical Society 1 Advances in Applied Mathematics 1 Graphs and Combinatorics 1 $$K$$-Theory 1 Publicacions Matemàtiques 1 Forum Mathematicum 1 Sugaku Expositions 1 International Journal of Algebra and Computation 1 Differential Geometry and its Applications 1 Geometric and Functional Analysis. GAFA 1 Annals of Physics 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 Annales Mathématiques Blaise Pascal 1 Documenta Mathematica 1 Transformation Groups 1 Annals of Mathematics. Second Series 1 Annales Henri Poincaré 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 Oberwolfach Reports 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Groups, Geometry, and Dynamics 1 Journal of Topology and Analysis 1 Japanese Journal of Mathematics. 3rd Series 1 Science China. Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Proceedings of the International Geometry Center 1 Forum of Mathematics, Sigma 1 EMS Surveys in Mathematical Sciences 1 Bollettino dell’Unione Matematica Italiana
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#### Cited in 35 Fields

 98 Group theory and generalizations (20-XX) 98 Manifolds and cell complexes (57-XX) 60 Nonassociative rings and algebras (17-XX) 54 Several complex variables and analytic spaces (32-XX) 51 Algebraic topology (55-XX) 50 Quantum theory (81-XX) 48 Algebraic geometry (14-XX) 27 Associative rings and algebras (16-XX) 23 Convex and discrete geometry (52-XX) 18 Special functions (33-XX) 13 Differential geometry (53-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Category theory; homological algebra (18-XX) 9 Commutative algebra (13-XX) 9 Partial differential equations (35-XX) 8 Combinatorics (05-XX) 7 Number theory (11-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Ordinary differential equations (34-XX) 5 Functional analysis (46-XX) 4 $$K$$-theory (19-XX) 4 Difference and functional equations (39-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Functions of a complex variable (30-XX) 3 Fluid mechanics (76-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Topological groups, Lie groups (22-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)