We explore the dynamics of the action of the mapping class group in genus on the -character variety. We prove that this action is ergodic on the connected components of Euler class , as it was conjectured by Goldman. In the connected component of Euler class 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 posed by Bowditch.
"The modular action on -characters in genus 2." Duke Math. J. 165 (2) 371 - 412, 1 February 2016. https://doi.org/10.1215/00127094-3166522