Embedding relatively hyperbolic groups in products of trees

作者：Mackay John M^*; Sisto Alessandro

来源：Algebraic and Geometric Topology, 2013, 13(4): 2261-2282.

DOI：10.2140/agt.2013.13.2261

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.

• 出版日期2013