Mutant knots with symmetry

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dc.creatorMorton, H. R.
dc.date2007-05-09
dc.date.accessioned2026-07-07T12:57:53Z
dc.date.available2026-07-07T12:57:53Z
dc.descriptionMutant 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.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0705.1321
dc.identifierhttp://arxiv.org/abs/0705.1321
dc.identifierMathematical Proceedings of the Cambridge Philosophical Society 146 (2009), 95-107
dc.identifierdoi:10.1017/S0305004108001862
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225060
dc.subjectGeometric Topology
dc.subject57M25
dc.titleMutant knots with symmetry
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