Invariants of genus 2 mutants

Details Invariants of genus 2 mutants Invariants of genus 2 mutants

2007-08-03

arxiv.org/abs/0708.0514v1

J.Knot Theor.Ramifications 18:1423-1438,2009

Mathematics

Geometric Topology

16 pages, 20 figures

Scientific paper

10.1142/S0218216509007506

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.

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