The Boundary at Infinity of the Curve Complex and the Relative Teichmüller Space

2018/03/27 by Erica Klarreich, Klarreich, Erica · 3 citations
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1803.10339

openalex publication_date 2018/03/27 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

In this paper we study the boundary at infinity of the curve complex C(S) of a surface S of finite type and the relative Teichmüller space T_el(S) obtained from the Teichmüller space by collapsing each region where a simple closed curve is short to be a set of diameter 1. C(S) and T_el(S) are quasi-isometric, and Masur-Minsky have shown that C(S) and T_el(S) are hyperbolic in the sense of Gromov. We show that the boundary at infinity of C(S) and T_el(S) is the space of topological equivalence classes of minimal foliations on S.

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