Mutant knots with symmetry

Details Mutant knots with symmetry Mutant knots with symmetry

2007-05-09

arxiv.org/abs/0705.1321v1

Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), 95-107

Mathematics

Geometric Topology

15 pages

Scientific paper

10.1017/S0305004108001862

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.

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