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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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S02...

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
ID Code:2998
Deposited By:Converis
Deposited On:12 Nov 2007
Last Modified:08 Oct 2013 12:06

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