English

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