Jones polynomial invariants

FISH, ANDREW and Keyman, Ebru (2006) Jones polynomial invariants Journal of Knot Theory and Its Ramifications, 15 (3). pp. 339-350. ISSN 0218-2165

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Abstract

The Jones polynomial is a well-defined invariant of virtual links. We observe the effect of a generalised mutation M of a link on the Jones polynomial. Using this, we describe a method for obtaining invariants of links which are also invariant under M . The Jones polynomial of welded links is not well-defined in Z[q 1/4 , q −1/4 ]. Taking M = Fo allows us to pass to a quotient of Z[q 1/4 , q −1/4 ] in which the Jones polynomial is well-defined. We get the same result for M = Fu , so in fact, the Jones polynomial in this ring defines a fused isotopy invariant. We show it is non-trivial and compute it for links with one or two components.

Item Type: Journal article
Additional Information: © 2006 World Scientific Publishing Company
Uncontrolled Keywords: Virtual links; Welded links; Jones polynomial
Subjects: G000 Computing and Mathematical Sciences > G100 Mathematics
DOI (a stable link to the resource): 10.1142/S0218216506004518
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
Depositing User: Converis
Date Deposited: 12 Nov 2007
Last Modified: 21 May 2014 11:01
URI: http://eprints.brighton.ac.uk/id/eprint/2998

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