Mutant knots with symmetry

Morton, HR ORCID: 0000-0002-8524-2695
(2009) Mutant knots with symmetry. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 146 (1). pp. 95-107.

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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.

Item Type: Article
Additional Information: 15 pages
Uncontrolled Keywords: math.GT, math.GT, 57M25
Depositing User: Symplectic Admin
Date Deposited: 26 Jan 2016 08:54
Last Modified: 16 Dec 2022 12:56
DOI: 10.1017/S0305004108001862
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