Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial

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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.
To appear in J. Combin. Theory Ser. B (2009), doi:10.1016/j.jctb.2008.09.007

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Combinatorics, Geometric Topology, 05C10; 57M15; 57M27

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http://salesiana.dossiersoluciones.com/handle/123456789/210585

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.3490
 http://arxiv.org/abs/0711.3490

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arXiv