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arXiv:math/0609012 [math.GT]AbstractReferencesReviewsResources

The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial

Sergei Chmutov, Igor Pak

Published 2006-09-01Version 1

We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollob\'as-Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes Thistlethwaite's celebrated theorem relating the Kauffman bracket with the Tutte polynomial of planar graphs.

Comments: This is a completely rewritten version of the previos preprint math.GT/0404475 oriented to topological applications to virtual links. To be published in the Moscow Mathematical Journal
Categories: math.GT, math.CO
Subjects: 57M25, 05C10
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arXiv:math/0404475 [math.GT] (Published 2004-04-27, updated 2004-06-02)
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