Non-semisimple invariants and Habiro's series
Geometric Topology
2020-09-29 v1 Quantum Algebra
Abstract
In this paper we establish an explicit relationship between Habiro's cyclotomic expansion of the colored Jones polynomial (evaluated at a p-th root of unity) and the Akutsu-Deguchi-Ohtsuki (ADO) invariants of the double twist knots. This allows us to compare the Witten-Reshetikhin-Turaev (WRT) and Costantino-Geer-Patureau (CGP) invariants of 3-manifolds obtained by 0-surgery on these knots. The difference between them is determined by the p-1 coefficient of the Habiro series. We expect these to hold for all Seifert genus 1 knots.
Keywords
Cite
@article{arxiv.2009.13285,
title = {Non-semisimple invariants and Habiro's series},
author = {Anna Beliakova and Kazuhiro Hikami},
journal= {arXiv preprint arXiv:2009.13285},
year = {2020}
}
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13 pages