INVARIANTS OF GENUS 2 MUTANTS

Morton, HR ORCID: 0000-0002-8524-2695 and Ryder, N (2009) INVARIANTS OF GENUS 2 MUTANTS. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 18 (10). pp. 1423-1438.

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Abstract

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 3-variable polynomials, answering a question raised by Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v=s^2, we give examples whose Homfly polynomials differ when v=s^3. We also give examples which differ in a Vassiliev invariant of degree 7, in contrast to satellites of Conway mutant knots.

Item Type:	Article
Additional Information:	16 pages, 20 figures
Uncontrolled Keywords:	Conway mutant, genus 2 mutant, Kauffman polynomial, Homfly polynomial, satellite, Vassiliev invariant
Depositing User:	Symplectic Admin
Date Deposited:	22 Feb 2016 12:24
Last Modified:	29 May 2023 21:10
DOI:	10.1142/S0218216509007506
Publisher's Statement :	Preprint of an article published in [Journal of Knot Theory and its Ramifications, 18, 10, 2009, 1423-1438] [10.1142/S0218216509007506] © [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/jktr]
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2052139