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• W2080137701 abstract "We introduce a polynomial invariant of graphs on surfaces, $P_G$, generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result for $P_G$, analogous to the duality for the Tutte polynomial of planar graphs. This property is important from the perspective of statistical mechanics, where the Tutte polynomial is known as the partition function of the Potts model. For ribbon graphs, $P_G$ specializes to the well-known Bollobas-Riordan polynomial, and in fact the two polynomials carry equivalent information in this context. Duality is also established for a multivariate version of the polynomial $P_G$. We then consider a 2-variable version of the Jones polynomial for links in thickened surfaces, taking into account homological information on the surface. An analogue of Thistlethwaite's theorem is established for these generalized Jones and Tutte polynomials for virtual links." @default.
• W2080137701 created "2016-06-24" @default.
• W2080137701 creator A5030453811 @default.
• W2080137701 date "2009-03-31" @default.
• W2080137701 modified "2023-09-27" @default.
• W2080137701 title "Graphs, links, and duality on surfaces" @default.
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