English

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

R2 v1 2026-06-21T09:04:38.693Z