American Mathematical Society (AMS) meeting #1037,
     Louisiana State University, Baton Rouge (LA), March 29, 2008.
     

Title: Duality of graphs on surfaces and Thistlethwaite's type theorems.

Author: Sergei V Chmutov

Abstract: The natural duality of graphs embedded into a surface can be
generalized to a duality with respect to a subset of edges. The dual graph
might be embedded into a different surface. For graphs on surfaces there is
a generalization of the classical Tutte polynomial called the
Bollobas-Riordan polynomial. I will explain a relation between the signed
Bollobas-Riordan polynomials of dual graphs. This relation unifies various
recent Thistlethwaite's type results of expressing the Jones polynomial of
(virtual) links as specializations of the Bollobas-Riordan polynomials.