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Embedding universal covers of graph manifolds in products of trees


Authors: David Hume and Alessandro Sisto
Journal: Proc. Amer. Math. Soc. 141 (2013), 3337-3340
MSC (2010): Primary 20F65, 20F69, 57M99
DOI: https://doi.org/10.1090/S0002-9939-2013-11669-2
Published electronically: June 14, 2013
MathSciNet review: 3080156
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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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Additional Information

David Hume
Affiliation: Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, United Kingdom
Email: hume@maths.ox.ac.uk

Alessandro Sisto
Affiliation: Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, United Kingdom
Email: sisto@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2013-11669-2
Received by editor(s): December 12, 2011
Published electronically: June 14, 2013
Additional Notes: This work is in the public domain
Communicated by: Alexander N. Dranishnikov