The modular action on PSL(2,R)-characters in genus 2

Abstract

We explore the dynamics of the action of the mapping class group in genus 2 on the PSL(2,R)-character variety. We prove that this action is ergodic on the connected components of Euler class 1 and -1, as it was conjectured by Goldman. In the connected component of Euler class 0 there are two invariant open subsets, on one of them the action is ergodic. In this process we give a partial answer to a question of Bowditch.

43 pages, 17 figures

References in corpus (2)

• Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces
• Dynamics on character varieties: a survey

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