Constructing group actions on quasi-trees and applications to mapping class groups

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, rank 1 CAT(0) groups, mapping class groups and Out(Fn). As an application, we show that mapping class groups act on finite products of {\delta}-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. We prove that mapping class groups have finite asymptotic dimension.

• Publication year

  2010

• Venue

  Unknown venue

• Publication date

  2010-06-10

• Fields of study

  Mathematics

• Identifiers
  arXiv 1006.1939
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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