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Graduate Student Geometry-Topology Seminar

Monday, September 12, 2022 - 4:30pm

Yi Wang



University of Pennsylvania

DRL 4N49

Let G be a complex semisimple Lie group, and let M be a topological space. The G-character variety of S, roughly speaking, is the space of conjugacy classes of representations from pi_1(M) to G. In the case where M is a surface, we get an action of Out(pi_1(M)) on the character variety. We will survey various results about this action, with the following motivating question: to what extent does Out(pi_1(M)) act properly discontinuously on the character variety? This talk will involve some topology, some algebra, and some analysis, which will likely either satisfy or upset the entire audience.