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

2004/04/27 by Sergei Chmutov, Chmutov, Sergei, Igor Pak +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GT #msc:05C10 #msc:05C15 #msc:57M15 #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0404475

Some references added

arxiv created 2004/06/02 · arxiv updated 2016/09/07

Abstract

For a ribbon graph G we consider an alternating link L_G in the 3-manifold G× 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.

Cited by

• A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan
• The Jones polynomial and graphs on surfaces

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