Embedding universal covers of graph manifolds in products of trees
Geometric Topology
2012-04-18 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1112.0263,
title = {Embedding universal covers of graph manifolds in products of trees},
author = {David Hume and Alessandro Sisto},
journal= {arXiv preprint arXiv:1112.0263},
year = {2012}
}
Comments
3 pages, final version - to appear in Proceedings of the AMS