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

摘要

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