Constructing group actions on quasi-trees and applications to mapping class groups
Group Theory
2014-09-09 v5 Geometric Topology
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 {\delta}-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. We prove that mapping class groups have finite asymptotic dimension.
Keywords
Cite
@article{arxiv.1006.1939,
title = {Constructing group actions on quasi-trees and applications to mapping class groups},
author = {Mladen Bestvina and Kenneth Bromberg and Koji Fujiwara},
journal= {arXiv preprint arXiv:1006.1939},
year = {2014}
}
Comments
The significant mathematical change is the statement and proof of Proposition 3.23 has been corrected. The introduction has been expanded and there has been a general improvement of the exposition following comments from the referees