Geometric triangulations and the Teichmüller TQFT volume conjecture for twist knots

Quantum topology

article

Fathi Ben Aribi¹  François Guéritaud²  Eiichi Piguet-Nakazawa³ 

[1] UCLouvain;Université de Strasbourg;Université de Genève

关键词: Triangulations;    twist knots;    3-manifolds;    hyperbolic volume;    Teichmüller TQFT;    volume conjecture;    saddle point method;   

DOI  :  10.4171/qt/178

学科分类：内科医学

来源: European Mathematical Society

【 摘 要 】

We construct a new infinite family of ideal triangulations and H–triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations provide a new upper bound for the Matveev complexity of twist knot complements. We then prove that these ideal triangulations are geometric. The proof uses techniques of Futer and the second author, which consist in studying the volume functional on the polyhedron of angle structures. Finally, we use these triangulations to compute explicitly the partition function of the Teichmüller TQFT and to prove the associated volume conjecture for all twist knots, using the saddle point method.

【 授权许可】

CC BY