Invariants of genus 2 mutants
Geometric Topology
2009-12-04 v1
Abstract
Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 3-variable polynomials, answering a question raised by Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v=s^2, we give examples whose Homfly polynomials differ when v=s^3. We also give examples which differ in a Vassiliev invariant of degree 7, in contrast to satellites of Conway mutant knots.
Cite
@article{arxiv.0708.0514,
title = {Invariants of genus 2 mutants},
author = {H. R. Morton and N. Ryder},
journal= {arXiv preprint arXiv:0708.0514},
year = {2009}
}
Comments
16 pages, 20 figures