Boundary representations of mapping class groups

Biao Ma

Boundary representations of mapping class groups

Geometric Topology 2022-09-13 v2 Dynamical Systems Representation Theory

Authors: Biao Ma

Abstract

Let $S = S_g$ be a closed orientable surface of genus $g \geq 2$ and $Mod(S)$ be the mapping class group of $S$ . In this paper, we show that the boundary representation of $Mod(S)$ is ergodic using statistical hyperbolicity, which generalizes the classical result of Masur on ergodicity of the action of $Mod(S)$ on the projective measured foliation space $\mathcal{PMF}(S).$ As a corollary, we show that the boundary representation of $Mod(S)$ is irreducible.

Keywords

mapping class groups of surfaces group representations representation theory of groups

Cite

@article{arxiv.2208.10223,
  title  = {Boundary representations of mapping class groups},
  author = {Biao Ma},
  journal= {arXiv preprint arXiv:2208.10223},
  year   = {2022}
}

Comments

The proof of Corollary 4.3 in the previous version is incorrect, hence section 4.3 has been rewritten. Section 3 and section 4.1 have also been reorganized. Comments welcome

Boundary representations of mapping class groups

Abstract

Keywords

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