The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs

Sergei Chmutov; Igor Pak

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The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs

Sergei Chmutov·Igor Pak

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Abstract

For a ribbon graph $G$ we consider an alternating link $L_G$ in the 3-manifold $G\times I$ represented as the product of the oriented surface $G$ and the unit interval $I$. We show that the Kauffman bracket $[L_G]$ is an evaluation of the recently introduced Bollobas-Riordan polynomial $R_G$. This results generalizes the celebrated relation between Kauffman bracket and Tutte polynomial of planar graphs.

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BibTeX RIS

Sergei Chmutov, Igor Pak. 2004-06-02. The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs. https://arxiv.org/abs/math/0404475

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