Mersenne banner

Winter Braids Lecture Notes

Browse issues
or
  • All
  • Author
  • Title
  • References
  • Full text
NOT
Between and
  • All
  • Author
  • Title
  • Date
  • References
  • Full text
  • Previous
  • Browse issues
  • Volume 3 (2016)
  • Talk no. 2
  • Next
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, Volume 3 (2016), Talk no. 2, 16 p.
  • Abstract

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 information
  • Export
  • How to cite
Published online: 2017-06-19
MR: 3707743 | Zbl: 1422.57077
DOI: 10.5802/wbln.13
Author's affiliations:
Rinat Kashaev 1

1 Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Suisse
  • BibTeX
  • RIS
  • EndNote
@article{WBLN_2016__3__A2_0,
     author = {Rinat Kashaev},
     title = {Combinatorics of the {Teichm\"uller} {TQFT}},
     journal = {Winter Braids Lecture Notes},
     note = {talk:2},
     publisher = {Winter Braids School},
     volume = {3},
     year = {2016},
     doi = {10.5802/wbln.13},
     mrnumber = {3707743},
     zbl = {1422.57077},
     language = {en},
     url = {https://wbln.centre-mersenne.org/articles/10.5802/wbln.13/}
}
TY  - JOUR
TI  - Combinatorics of the Teichmüller TQFT
JO  - Winter Braids Lecture Notes
N1  - talk:2
PY  - 2016
DA  - 2016///
VL  - 3
PB  - Winter Braids School
UR  - https://wbln.centre-mersenne.org/articles/10.5802/wbln.13/
UR  - https://www.ams.org/mathscinet-getitem?mr=3707743
UR  - https://zbmath.org/?q=an%3A1422.57077
UR  - https://doi.org/10.5802/wbln.13
DO  - 10.5802/wbln.13
LA  - en
ID  - WBLN_2016__3__A2_0
ER  - 
%0 Journal Article
%T Combinatorics of the Teichmüller TQFT
%J Winter Braids Lecture Notes
%Z talk:2
%D 2016
%V 3
%I Winter Braids School
%U https://doi.org/10.5802/wbln.13
%R 10.5802/wbln.13
%G en
%F WBLN_2016__3__A2_0
Rinat Kashaev. Combinatorics of the Teichmüller TQFT. Winter Braids Lecture Notes, Volume 3 (2016), Talk no. 2, 16 p. doi : 10.5802/wbln.13. https://wbln.centre-mersenne.org/articles/10.5802/wbln.13/
  • References
  • Cited by

[1] Jørgen Ellegaard Andersen and Rinat Kashaev. A TQFT from Quantum Teichmüller Theory. Comm. Math. Phys., 330(3):887–934, 2014. | Article | Zbl: 1305.57024

[2] Stéphane Baseilhac and Riccardo Benedetti. Quantum hyperbolic invariants of 3-manifolds with PSL (2,ℂ)-characters. Topology, 43(6):1373–1423, 2004. | Article | MR: 2081430 | Zbl: 1065.57008

[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. | Article | MR: 3486430 | Zbl: 1337.81105

[4] Rinat M. Kashaev. On realizations of Pachner moves in 4d. J. Knot Theory Ramifications, 24(13):1541002, 13, 2015. | Article | MR: 3434541 | Zbl: 1337.57064

[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. | Article | Zbl: 0963.57013

[6] S. V. Matveev. Transformations of special spines, and the Zeeman conjecture. Izv. Akad. Nauk SSSR Ser. Mat., 51(5):1104–1116, 1119, 1987. | Article | MR: 925096 | Zbl: 0642.57003

[7] Sergei Matveev. Algorithmic topology and classification of 3-manifolds, volume 9 of Algorithms and Computation in Mathematics. Springer-Verlag, Berlin, 2003. | Article | Zbl: 1048.57001

[8] John Milnor. Hyperbolic geometry: the first 150 years. Bull. Amer. Math. Soc. (N.S.), 6(1):9–24, 1982. | Article | MR: 634431 | Zbl: 0486.01006

[9] Udo Pachner. P.L. homeomorphic manifolds are equivalent by elementary shellings. European J. Combin., 12(2):129–145, 1991. | Article | Zbl: 0729.52003

[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: 0672.57004

[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. | Article | Zbl: 0812.57003

[13] V. G. Turaev and O. Ya. Viro. State sum invariants of 3-manifolds and quantum 6j-symbols. Topology, 31(4):865–902, 1992. | Article | MR: 1191386 | Zbl: 0779.57009

Cited by Sources:

Web publisher : Published by : Developed by :
  • Follow us
e-ISSN : 2426-0312
© 2014 - 2022 Centre Mersenne, Winter Braids Lecture Notes, and the authors