English

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

R2 v1 2026-06-22T01:26:47.339Z