论文标题
映射课程组的边界表示
Boundary representations of mapping class groups
论文作者
论文摘要
令$ s = s_g $是$ g \ geq 2 $和$ mod（s）$的封闭式定向表面，为$ s $的映射类组。在本文中，我们表明，$ mod（s）$的边界表示使用统计双曲线，它概括了MASUR对$ mod（s）$在投影测量的叶面范围$ \ Mathcal $ \ Mathcal {pmf}（pmf}（s）的作用的经典结果，我们显示了$ mod $ rifectibal $ irecrib y Ir rifecrib（s）。
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.
