Embedding relatively hyperbolic groups in products of trees

John M. Mackay, Alessandro Sisto

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2261-2282
Number of pages22
JournalAlgebraic and Geometric Topology
Volume13
Issue number4
DOIs
Publication statusPublished - 19 Jun 2013

ASJC Scopus subject areas

  • Geometry and Topology

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