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. 
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