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 = 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.

Locations

• arXiv (Cornell University) - View - PDF
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• Journal of Knot Theory and Its Ramifications - View