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

Abstract

We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollobás-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.

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