Dubois' Torsion, A-polynomial and Quantum Invariants
Geometric Topology
2011-01-17 v1 Quantum Algebra
Abstract
It is shown that for knots with a sufficiently regular character variety the Dubois' torsion detects the A-polynomial of the knot. A global formula for the integral of the Dubois torsion is given. The formula looks like the heat kernel regularization of the formula for the Witten-Reshetikhin-Turaev invariant of the double of the knot complement. The Dubois' torsion is recognized as the pushforward of a measure on the character variety of the double of the knot complement coming from the square root of Reidemeister torsion. This is used to motivate a conjecture about quantum invariants detecting the A-polynomial.
Keywords
Cite
@article{arxiv.1101.2695,
title = {Dubois' Torsion, A-polynomial and Quantum Invariants},
author = {Charles Frohman and Joanna Kania-Bartoszynska},
journal= {arXiv preprint arXiv:1101.2695},
year = {2011}
}
Comments
34 pages, 3 figures