2:00 pm Monday, November 19, 2012
Topology Seminar: A pressure metric for the Hitchin component by Dick Canary (University of Michigan) in RLM 12.166
Hitchin exhibited components of the space of (conjugacy classes of) representations of a closed surface group into PSL(n,R) which are homeomorphic to balls. Labourie showed that the representations in these components are discrete and faithful and that mapping class groups act properly discontinuously on Hitchin components. Hence, Hitchin components are natural generalizations of Teichmuller spaces. In collaboration with Bridgeman, Labourie and Sambarino, we have used the thermodynamic formalism to construct a mapping class group invariant analytic Riemannian metric on each Hitchin component whose restriction to the Fuchsian locus is a multiple of the Weil-Petersson metric. Our techniques apply to give metrics on more general deformation spaces and to show that the Hausdorff dimension of the limit set varies analytically over deformation spaces of convex cocompact Kleinian groups. Submitted by
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