2015/12/07 by Julien Marché, Maxime Wolff
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry
paper · doi:10.1215/00127094-3166522
We explore the dynamics of the action of the mapping class group in genus 2 on the PSL2(R)-character variety. We prove that this action is ergodic on the connected components of Euler class ±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 posed by Bowditch.