2:00 pm Monday, February 3, 2014
Topology Seminar: Surface groups, representation spaces, and rigidity by Kathryn Mann (University of Chicago) in RLM 12.166
Let S_g denote the closed, genus g surface. In this talk, we'll discuss the space of all circle bundles over S_g, Hom(pi_1(S_g), Homeo+(S^1)). The Milnor-Wood inequality gives a lower bound on the number of components of this space (4g-3), but until very recently it was not known whether this bound was sharp. In fact, we still don't know whether the space has infinitely many components! I'll report on recent work and new tools to understand Hom(\pi_1(S_g), Homeo+(S^1)). In particular, I use dynamical methods to give a new lower bound on the number of components, and show that certain geometric representations are surprisingly rigid. Submitted by
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