Embedding relatively hyperbolic groups in products of trees
Geometric Topology
2014-10-01 v2 Group Theory
Abstract
We show that a relatively hyperbolic group quasi-isometrically embeds in a product of finitely many trees if the peripheral subgroups do, and we provide an estimate on the minimal number of trees needed. Applying our result to the case of 3-manifolds, we show that fundamental groups of closed 3-manifolds have linearly controlled asymptotic dimension at most 8. To complement this result, we observe that fundamental groups of Haken 3-manifolds with non-empty boundary have asymptotic dimension 2.
Cite
@article{arxiv.1207.3008,
title = {Embedding relatively hyperbolic groups in products of trees},
author = {John M. Mackay and Alessandro Sisto},
journal= {arXiv preprint arXiv:1207.3008},
year = {2014}
}
Comments
v1: 18 pages; v2: 20 pages, minor changes