Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial
Combinatorics
2008-12-16 v3 Geometric Topology
Abstract
We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the Jones polynomial of links as specializations of the Bollobas-Riordan polynomials.
Keywords
Cite
@article{arxiv.0711.3490,
title = {Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial},
author = {Sergei Chmutov},
journal= {arXiv preprint arXiv:0711.3490},
year = {2008}
}
Comments
To appear in J. Combin. Theory Ser. B (2009), doi:10.1016/j.jctb.2008.09.007