Covers and the curve complex

Abstract

We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either by puncturing a closed surface or via orbifold coverings. As a corollary, we give new quasi-isometric embeddings between mapping class groups.

12 pages, no figures. Added application to mapping class groups

Cited by in corpus (11)

• Random walks on the mapping class group
• Uniform hyperbolicity of the curve graph via surgery sequences
• Convex cocompactness and stability in mapping class groups
• Hyperbolicity in Teichmüller space
• Curve complexes are rigid
• Large scale rank of Teichmuller space
• Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations
• The curve complex and covers via hyperbolic 3-manifolds
• Random walks and contracting elements I: Deviation inequality and Limit laws
• The mapping class group of a nonorientable surface is quasi-isometrically embedded in the mapping class group of the orientation double cover
• Projections in the curve complex arising from covering maps