Embedding relatively hyperbolic groups in products of trees

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.

• Publication year

  2012

• Venue

  arXiv: Geometric Topology

• Publication date

  2012-07-12

• Fields of study

  Mathematics

• Identifiers
  DOI 10.2140/agt.2013.13.2261arXiv 1207.3008
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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