The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere
Geometric Topology
2024-06-04 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We compute the Bonahon-Wong-Yang quantum invariant for self-diffeomorphisms of the four-puncture sphere explicitly, based on the representation theory of the Checkov-Fock algebra. As an application of the computation, we verify the volume conjecture proposed by Bonahon-Wong-Yang for the four puncture sphere bundles with some technical conditions. Together with the one-puncture torus bundles, this is the first family of examples for which the conjecture is verified providing evidence for the conjecture
Keywords
Cite
@article{arxiv.2311.13151,
title = {The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere},
author = {Tushar Pandey},
journal= {arXiv preprint arXiv:2311.13151},
year = {2024}
}