The modular action on PSL(2,R)-characters in genus 2
Geometric Topology
2016-02-10 v1 Differential Geometry
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.
Cite
@article{arxiv.1309.3553,
title = {The modular action on PSL(2,R)-characters in genus 2},
author = {Julien Marché and Maxime Wolff},
journal= {arXiv preprint arXiv:1309.3553},
year = {2016}
}
Comments
43 pages, 17 figures