The boundary at infinity of the curve complex and the relative Teichmüller space
The boundary at infinity of the curve complex and the relative Teichmüller space
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DOI：
10.4171/ggd/662
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发表时间：
2018-03
期刊：
影响因子：
--
通讯作者：
E. Klarreich
中科院分区：
文献类型：
--
作者：
E. Klarreich
In this paper we study the boundary at infinity of the curve complex $\mathcal{C}(S)$ of a surface $S$ of finite type and the relative Teichm\"{u}ller space $\mathcal{T}_{el}(S)$ obtained from the Teichm\"{u}ller space by collapsing each region where a simple closed curve is short to be a set of diameter 1. $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ are quasi-isometric, and Masur-Minsky have shown that $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ are hyperbolic in the sense of Gromov. We show that the boundary at infinity of $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ is the space of topological equivalence classes of minimal foliations on $S$.
In this paper we study the boundary at infinity of the curve complex $\mathcal{C}(S)$ of a surface $S$ of finite type and the relative Teichm\"{u}ller space $\mathcal{T}_{el}(S)$ obtained from the Teichm\"{u}ller space by collapsing each region where a simple closed curve is short to be a set of diameter 1. $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ are quasi-isometric, and Masur-Minsky have shown that $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ are hyperbolic in the sense of Gromov. We show that the boundary at infinity of $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ is the space of topological equivalence classes of minimal foliations on $S$.