DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS



MORTON, HUGH R and CROMWELL, PETER R
(1996) DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS. Journal of Knot Theory and Its Ramifications, 05 (02). 225 - 238.

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Abstract

<jats:p> We consider the problem of distinguishing mutant knots using invariants of their satellites. We show, by explicit calculation, that the Homfly polynomial of the 3-parallel (and hence the related quantum invariants) will distinguish some mutant pairs. </jats:p><jats:p> Having established a condition on the colouring module which forces a quantum invariant to agree on mutants, we explain several features of the difference between the Homfly polynomials of satellites constructed from mutants using more general patterns. We illustrate this by our calculations; from these we isolate some simple quantum invariants, and a framed Vassiliev invariant of type 11, which distinguish certain mutants, including the Conway and Kinoshita-Teresaka pair. </jats:p>

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 21 Apr 2016 11:20
Last Modified: 09 Jan 2021 08:31
DOI: 10.1142/s0218216596000163
URI: https://livrepository.liverpool.ac.uk/id/eprint/3000698