List of Publications


Toshitake Kohno

  • Differential forms and the fundamental group of the complement of hypersurfaces, Proc. Symp. in Pure Math. AMS 40-1 (1982) 655--662.

  • On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces, Nagoya Math. J. 92 (1983) 21--37.

  • An algebraic computation of the Alexander polynomial of a plane algebraic curve, Proc. Japan Acad. 59, Ser. A (1983) 94--97

  • Série de Poincaré-Koszul associée aux groupes de tresses pures, Invent. Math. 82 (1985) 57--75

  • Homology of a local system on the complement of hyperplanes, Proc. Japan Acad. 62, Ser. A (1986) 144--147.

  • One-parameter family of linear representations of Artin's braid groups, Advanced Studies in Pure Math. 12 (1987) 189--200.

  • (with Takayuki Oda) The lower central series of the pure braid group of an algebraic curve, Advanced Studies in Pure Math. 12 (1987) 255--269.

  • Hecke algebra representations of braid groups and classical Yang-Baxter equations, Advanced Studies in Pure Math. 16 (1987) 189--200.

  • Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier 37-4 (1987) 139--160.

  • Linear representations of braid groups and classical Yang-Baxter equations, Contemp. Math. 78 (1988) 339--363.

  • Monodromy of braid groups in conformal field theory on P1 and Yang-Baxter equations, Proc. of the 3rd Asia-Pacific Conference of Physics (1988) 339--363.

  • Integrable systems related to braid groups and Yang-Baxter equation, Braid Group, Knot Theory and Statistical Mechanics, eds. C. N. Yang and M. L. Ge (1989) 135--150.

  • Monodromy of braid groups in conformal field theory and positive Markov traces, Differential Geometric Methods in Theoretical Physics, eds. A. I. Solomon (1989) 64--73.

  • Fusion in the monodromy of braid groups , Proc. of Nankai workshop, World Scientific (1989) .

  • Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups, Contemp. Math. 90 (1989) 171--182.

  • Integrable connections related to Manin and Schechtman's higher braid groups, Illinois J. of Math. 34-2 (1990) 476--484.

  • Quantized universal enveloping algebras and monodromy of braid groups, Nagoya University, preprint (1990).

  • Topological invariants for 3-manifolds using representations of mapping class groups I, Topology 31-2 (1992) 203--230.

  • Topological invariants of 3-manifolds based on conformal field theory and Heegaard splitting, "Quantum Groups", LNM 1510, Springer (1992) 341--349.

  • Three-manifold invariants derived from conformal field theory and projective representations of modular groups, International Journal of Modern Physics 6 (1992) 1795--1805.

  • (with T. Takata) Symmetry of Witten's 3-manifold invariants for sl(n,C), Journal of Knot Theory and Its Ramifications 2-2 (1993) 149--169.

  • Monodromy representations of braid groups, Sugaku Expositions 7-2 (1994) 117--141.

  • Topological invariants for 3-manifolds using representations of mapping class groups II: Estimating tunnel number of knots, Contemp. Math. Amer.
    Math. Soc. 175 (1994) 193--217.

  • Tunnel numbers of knots and Jones-Witten invariants, "Braid group, knot theory and statistical mechanics II" Advanced Series in Mathematical Physics17 (1994) 275--293.

  • Monodromy representations of conformal field theory and their applications, "Geometry, Topology and Field Theory", Proceedings of the 31st International Taniguchi Symposium (1994) 67--78.

  • Vassiliev invariants and de Rham complex on the space of knots, Contemp. Math. Amer. Math. Soc. 179 (1994)123--138.

  • (with T. Takata) Level-rank duality of Witten's 3-manifold invariants Advanced Stud. Pure. Math. 24 (1996), 243--264.

  • Elliptic KZ system, braid group of the torus and Vassiliev invariants, Topology and its applications 20 (1997), 1--16.

  • Chern-Simons perturbative invariants, in "Lectures at Knots 96" edited by S. Suzuki. (1997), 235 -- 261

  • Monodromy of conformal blocks, Proc. Appl. Math. Workshops KAIST (1997), 179 -- 186

  • Topological quantum field theories with focus on their applications to 3-manifolds, Sugaku Expositions 11-2, Amer. Math. Soc. (1998), 145 -- 161.

  • Vassiliev invariants of braids and iterated integrals, Advanced Studuies in Pure Math. 27 (2000), 157--168.

  • Bar complex of the Orlik-Solomon algebra, Topology and its applications 118 (2002) 147 -- 157.

  • Conformal field theory and topology, Translations of Mathematical Monographs, Volume 210 American Mathematical Society, 2002, 182 pages.

  • Loop spaces of configuration spaces and finite type invariants, Geometry and Topology Monographs, Vol. 4 (2002), Invariants of knots and 3-manifolds (Kyoto 2001), Paper no. 10, pages 143--160.

  • Braids, hypergeometric integrals and conformal field theory, Proceedings of the First East Asian School of Knots, Links and Related Topics (2004).

  • The volume of a hyperbolic simplex and iterated integrals, Series on Knots and Everything 40 (2007) 179--188.

  • Loop spaces of configuration spaces and link homotopy invariants, Proceedings of East Asian Conference on Algebraic Topology (2007) .

  • (with F. R. Cohen and M. A. Xicotencatl) Orbit configuration spaces associated to discrete subgroups of PSL(2, R), Journal of Pure and Applied Algebra, 213, (2009), 2289 -- 2300.

  • Bar complex, configuration spaces and finite type invariants for braids, Topology and Its Applications 157 (2010) 2--9.

  • (with L. Funar). On Burau representations at roots of unity.

  • Hyperplane arrangements, local system homology and iterated integrals, to appear in Advanced Studies in Pure Mathematics.

  • KZ equation - structure of monodromy representations and their applications to invariants of knots, Appendix to "Theory of Hypergeometric Functions" by Kazuhiko Aomoto amd Michitake Kita, Springer, (2010), 283--301.

  • (with A. J. Pajitnov), Circle-valued Morse theory for complex hyperplane arrangements, arXiv:1101.0437v1 [math.GT]

  • Quantum and homological representations of braid groups, to appear in Ann. Scuola Norm. Sup. Pisa.

  • (with L. Funar). Free subgroups within the images of quantum representations, arXiv:1108.4904 [math.GT], to appear in Forum Mathematicum.

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