Character varieties of surfaces and Kauffman brackets

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• Francis Bonahon, USC
• Wednesday 04 May 2011, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

My talk will involve two concepts which are apparently very different. The character variety of a surface S, consisting of homomorphisms from the fundamental group of S to a Lie group G, arises in many different branches of mathematics. The classical Kauffman bracket is an invariant of knots and links in space, closely related to the Jones polynomial. When G = SL_2 C, Turaev showed that the character variety can be quantised by a generalisation of Kauffman brackets to the surface S. I will discuss the classification problem for Kauffman brackets on S, with results, conjectures and interesting examples.

This talk is part of the Differential Geometry and Topology Seminar series.

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