Embedding universal covers of graph manifolds in products of trees

2011/12/01 by David Hume, Alessandro Sisto, Hume, David +1
Mathematics · #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG #msc:20F65

paper · pdf · doi:10.48550/arxiv.1112.0263

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

arxiv created 2012/04/17 · arxiv updated 2012/04/18

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.

Related

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• Constructing Universal Abelian Covers of Graph Manifolds
• Embedding products of graphs into Euclidean spaces
• The Well-Covered Dimension of Products of Graphs