Published in |
Journal of Gökova Geometry Topology, Volume 3 (2009) |
Title |
Mutation and the colored Jones polynomial |
Author |
Alexander Stoimenow and Toshifumi Tanaka |
Abstract |
It is known that the colored Jones polynomials, various 2-cable link
polynomials, the hyperbolic volume, and the fundamental group of the double branched
cover coincide on mutant knots. We construct examples showing that these criteria,
even in various combinations, are not sufficient to determine the mutation class of a
knot, and that they are independent in several ways. In particular, we answer negatively the question of whether the colored Jones polynomial determines a simple knot up to mutation.
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Keywords |
Mutation, Jones polynomial, fundamental group, double branched cover,
concordance |
Pages | 44-78 |
Download |
PDF |
Submitted: | May 3, 2009 |
Accepted: | September 25, 2009 |
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