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.
@article{WBLN_2016__3__A2_0,
author = {Kashaev, Rinat},
title = {Combinatorics of the {Teichm\"uller} {TQFT}},
booktitle = {Winter Braids VI (Lille, 2016)},
series = {Winter Braids Lecture Notes},
note = {talk:2},
pages = {1--16},
publisher = {Winter Braids School},
year = {2016},
doi = {10.5802/wbln.13},
mrnumber = {3707743},
zbl = {1422.57077},
language = {en},
url = {http://www.numdam.org/articles/10.5802/wbln.13/}
}
TY - JOUR AU - Kashaev, Rinat TI - Combinatorics of the Teichmüller TQFT BT - Winter Braids VI (Lille, 2016) AU - Collectif T3 - Winter Braids Lecture Notes N1 - talk:2 PY - 2016 SP - 1 EP - 16 PB - Winter Braids School UR - http://www.numdam.org/articles/10.5802/wbln.13/ DO - 10.5802/wbln.13 LA - en ID - WBLN_2016__3__A2_0 ER -
%0 Journal Article %A Kashaev, Rinat %T Combinatorics of the Teichmüller TQFT %B Winter Braids VI (Lille, 2016) %A Collectif %S Winter Braids Lecture Notes %Z talk:2 %D 2016 %P 1-16 %I Winter Braids School %U http://www.numdam.org/articles/10.5802/wbln.13/ %R 10.5802/wbln.13 %G en %F WBLN_2016__3__A2_0
Kashaev, Rinat. Combinatorics of the Teichmüller TQFT, dans Winter Braids VI (Lille, 2016), Winter Braids Lecture Notes (2016), Exposé no. 2, 16 p. doi : 10.5802/wbln.13. http://www.numdam.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 -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 -manifolds and quantum -symbols. Topology, 31(4):865–902, 1992. | DOI | MR | Zbl
Cité par Sources :
