INVARIANTS OF GENUS 2 MUTANTS

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 2-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 = s2, we give examples whose Homfly polynomials differ when v = s3. We also give examples which differ in a Vassiliev invariant of degree 7, in contrast to satellites of Conway mutant knots.