# Embedding universal covers of graph manifolds in products of trees

@inproceedings{Hume2011EmbeddingUC, title={Embedding universal covers of graph manifolds in products of trees}, author={D. Hume and A. Sisto}, year={2011} }

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.

#### 6 Citations

Embedding relatively hyperbolic groups in products of trees

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We prove that for all p > 1, every relatively hyperbolic group has lp compression exponent equal to the minimum of the exponents of its maximal peripheral subgroups. This improves results of… Expand

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Embeddings of infinite groups into Banach spaces. David Hume, St Cross College. Submitted for the degree of Doctor of Philosophy, Hilary 2013. In this thesis we build on the theory concerning the… Expand

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Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of $3$--dimensional graph manifolds. In this… Expand

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