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Invariants of links and graphs

Sergei Chmutov
Ohio State University

Thursday, May 20, 2004
102 Bradley Hall, 4 pm
Tea 3:30 pm, Math Lounge

Abstract: I am going to discuss the following well known relation between knot theory and graph theory. The Jones polynomial of an alternating link is equal (up to a sign and a power of the variable) to the Tutte polynomial of the planar graph corresponding to a diagram of the link. We generalize this result to ribbon graphs (not necessarily planar) and links in certain 3-manifolds. We use the Bollobas-Riordan polynomial of ribbon graphs instead of the Tutte polynomial, and the Kauffman bracket as a version of the Jones polynomial. This is a joint work with Igor Pak (MIT).

This talk will be accessible to general faculty.