Embedding universal covers of graph manifolds in products of trees

Hume, David; Sisto, Alessandro

doi:10.1090/S0002-9939-2013-11669-2

Embedding universal covers of graph manifolds in products of trees
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by David Hume and Alessandro Sisto PDF

Proc. Amer. Math. Soc. 141 (2013), 3337-3340 Request permission

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.

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