Non-triviality of the A-polynomial for knots in S^3
Geometric Topology
2014-10-01 v3 Quantum Algebra
Abstract
The A-polynomial of a knot in S^3 defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL(2,C). Here, we show that a non-trivial knot in S^3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU_2-representations of Dehn surgeries on knots in S^3. As a corollary, we show that if a conjecture connecting the colored Jones polynomials to the A-polynomial holds, then the colored Jones polynomials distinguish the unknot
Keywords
Cite
@article{arxiv.math/0405353,
title = {Non-triviality of the A-polynomial for knots in S^3},
author = {Nathan M. Dunfield and Stavros Garoufalidis},
journal= {arXiv preprint arXiv:math/0405353},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-50.abs.html