Combinatorics of the Teichmüller TQFT
Rinat Kashaev1
1 Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Suisse
Winter Braids Lecture Notes, Winter Braids VI (Lille, 2016), Tome 3 (2016), Exposé no. 2, 16 p.

Based on the lectures given by the author at the School on braids and low dimensional topology “Winter Braids VI”, University of Lille I, 22-25 February 2016, we review the combinatorics underlying the Teichmüller TQFT, a new type of three-dimensional TQFT with corners where the vector spaces associated with surfaces are infinite dimensional. The geometrical ingredients and the semi-classical behaviour suggest that this theory is related with hyperbolic geometry in dimension three.

Publié le :
DOI : 10.5802/wbln.13
Rinat Kashaev 1

1 Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Suisse 
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Rinat Kashaev. Combinatorics of the Teichmüller TQFT. Winter Braids Lecture Notes, Winter Braids VI (Lille, 2016), Tome 3 (2016), Exposé no. 2, 16 p. doi : 10.5802/wbln.13. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.13/

[1] Jørgen Ellegaard Andersen and Rinat Kashaev. A TQFT from Quantum Teichmüller Theory. Comm. Math. Phys., 330(3):887–934, 2014. | DOI | Zbl

[2] Stéphane Baseilhac and Riccardo Benedetti. Quantum hyperbolic invariants of 3-manifolds with PSL (2,ℂ)-characters. Topology, 43(6):1373–1423, 2004. | DOI | MR | Zbl

[3] Rinat Kashaev, Feng Luo, and Grigory Vartanov. A TQFT of Turaev-Viro type on shaped triangulations. Ann. Henri Poincaré, 17(5):1109–1143, 2016. | DOI | MR | Zbl

[4] Rinat M. Kashaev. On realizations of Pachner moves in 4d. J. Knot Theory Ramifications, 24(13):1541002, 13, 2015. | DOI | MR | Zbl

[5] W. B. R. Lickorish. Simplicial moves on complexes and manifolds. In Proceedings of the Kirbyfest (Berkeley, CA, 1998), volume 2 of Geom. Topol. Monogr., pages 299–320 (electronic). Geom. Topol. Publ., Coventry, 1999. | DOI | Zbl

[6] S. V. Matveev. Transformations of special spines, and the Zeeman conjecture. Izv. Akad. Nauk SSSR Ser. Mat., 51(5):1104–1116, 1119, 1987. | DOI | MR | Zbl

[7] Sergei Matveev. Algorithmic topology and classification of 3-manifolds, volume 9 of Algorithms and Computation in Mathematics. Springer-Verlag, Berlin, 2003. | DOI | Zbl

[8] John Milnor. Hyperbolic geometry: the first 150 years. Bull. Amer. Math. Soc. (N.S.), 6(1):9–24, 1982. | DOI | MR | Zbl

[9] Udo Pachner. P.L. homeomorphic manifolds are equivalent by elementary shellings. European J. Combin., 12(2):129–145, 1991. | DOI | Zbl

[10] Riccardo Piergallini. Standard moves for standard polyhedra and spines. Rend. Circ. Mat. Palermo (2) Suppl., (18):391–414, 1988. Third National Conference on Topology (Italian) (Trieste, 1986). | Zbl

[11] G. Ponzano and T. Regge. Semiclassical limit of Racah coefficients. In Spectroscopic and group theoretical methods in physics, pages 1–58. North-Holland Publ. Co., Amsterdam, 1968.

[12] V. G. Turaev. Quantum invariants of knots and 3-manifolds, volume 18 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 1994. | DOI | Zbl

[13] V. G. Turaev and O. Ya. Viro. State sum invariants of 3-manifolds and quantum 6j-symbols. Topology, 31(4):865–902, 1992. | DOI | MR | Zbl

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