The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial

Sergei Chmutov; Igor Pak

The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial

Geometric Topology 2007-05-23 v1 Combinatorics

Authors: Sergei Chmutov , Igor Pak

Abstract

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.

Keywords

virtual links kauffman bracket bollobas-riordan polynomial ribbon graphs tutte polynomial

Cite

@article{arxiv.math/0609012,
  title  = {The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial},
  author = {Sergei Chmutov and Igor Pak},
  journal= {arXiv preprint arXiv:math/0609012},
  year   = {2007}
}

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

The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial

Abstract

Keywords

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