Boundary representations of mapping class groups

Biao Ma

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arXiv · 2208.10223

Boundary representations of mapping class groups

Biao Ma

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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.

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BibTeX RIS

Biao Ma. 2022-08-22. Boundary representations of mapping class groups. https://arxiv.org/abs/2208.10223

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