Embedding universal covers of graph manifolds in products of trees
  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. 
David Hume and Alessandro Sisto
math.GT math.MG