Embedding universal covers of graph manifolds in products of trees

Abstract

We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular we show that the Assouad-Nagata dimension of the universal cover of any closed graph manifold is 3, proving a conjecture of Smirnov.

arXiv comment3 pages, final version - to appear in Proceedings of the AMS

References in corpus (1)

• 3-manifold groups have unique asymptotic cones

Cited by in corpus (1)

• Direct embeddings of relatively hyperbolic groups with optimal ${\ell }^p$ compression exponent