Covers and the curve complex

2007/01/31 by Kasra Rafi, Saul Schleimer
Mathematics · Medicine · #Algebraic Geometry and Number Theory #Artificial intelligence #Class (philosophy) #Computer science #Corollary #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Isometric exercise #Mathematics #Medicine #Orbifold #Pure mathematics #Surface (topology) #math.GT #msc:30F99 #msc:57M99

paper · pdf · doi:10.2140/gt.2009.13.2141

published as Geom. Topol. 13 (2009) 2141-2162 · 12 pages, no figures. Added application to mapping class groups

arxiv created 2007/06/28 · openalex publication_date 2009/05/05 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We provide the first nontrivial examples of quasi-isometric embeddings between curve complexes; these are induced by orbifold covers. This leads to new quasiisometric embeddings between mapping class groups. As a corollary, in the mapping class group normalizers of finite subgroups are undistorted.

Citations

• Geometry of the complex of curves I: Hyperbolicity
• 3-Manifolds as viewed from the curve complex
• The Geometries of 3-Manifolds
• The Nielsen Realization Problem