Mutant knots with symmetry
Geometric Topology
2009-03-31 v1
Abstract
Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directed m-string satellites of mutants share the same Homfly polynomial for m<6 in general, and for all choices of m when the satellite is based on a cable knot pattern. We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantum sl(3) invariants.
Keywords
Cite
@article{arxiv.0705.1321,
title = {Mutant knots with symmetry},
author = {H. R. Morton},
journal= {arXiv preprint arXiv:0705.1321},
year = {2009}
}