Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots
Abstract
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 Teichm\"uller TQFT and to prove the associated volume conjecture for all twist knots, using the saddle point method.
Keywords
Cite
@article{arxiv.1903.09480,
title = {Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots},
author = {Fathi Ben Aribi and François Guéritaud and Eiichi Piguet-Nakazawa},
journal= {arXiv preprint arXiv:1903.09480},
year = {2022}
}
Comments
v5: 91 pages, 25 figures. Final version, accepted in Quantum Topology. Since v4, minor corrections were done and we added Example 2.8