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

2010/06/10 by Bestvina, Mladen, Bromberg, Kenneth, Fujiwara, Koji
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1006.1939

Abstract

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 δ-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. We prove that mapping class groups have finite asymptotic dimension.

Related

• Proper actions on finite products of quasi-trees
• Groups acting on hyperbolic spaces with a locally finite orbit
• Embedding mapping class groups into finite products of trees
• Quasi-actions whose quasi-orbits are quasi-isometric to trees
• Quasi-actions on trees I. Bounded valence