The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates
Geometric Topology
2024-10-18 v1 High Energy Physics - Theory
Abstract
We present an alternative definition of the twisted 1-loop invariant in terms of the Jacobian of Ptolemy coordinates. As an application, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This implies that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.
Keywords
Cite
@article{arxiv.2110.11003,
title = {The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates},
author = {Seokbeom Yoon},
journal= {arXiv preprint arXiv:2110.11003},
year = {2024}
}