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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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.
| 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 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/2048559 |
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