Author
Hume, D
Journal title
Groups, Geometry, and Dynamics
DOI
10.4171/GGD/410
Issue
2
Volume
11
Last updated
2024-03-21T14:47:56.567+00:00
Page
613-647
Abstract
We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-isometrically embed into a finite product of simplicial trees. In particular, these groups have finite Assouad–Nagata dimension, direct embeddings exhibiting ℓp compression exponent 1 for all p≥1 and they quasi-isometrically embed into ℓ1(\N). We deduce similar consequences for relatively hyperbolic groups whose parabolic subgroups satisfy such conditions. In obtaining these results we also demonstrate that curve complexes of compact surfaces and coned-off graphs of relatively hyperbolic groups admit quasi-isometric embeddings into finite products of trees.
Symplectic ID
701587
Favourite
Off
Publication type
Journal Article
Publication date
01 Jan 2017
Please contact us with feedback and comments about this page. Created on 22 Jun 2017 - 15:45.