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.References
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Additional Information
- David Hume
- Affiliation: Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, United Kingdom
- MR Author ID: 1029452
- ORCID: 0000-0003-2195-6071
- Email: hume@maths.ox.ac.uk
- Alessandro Sisto
- Affiliation: Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, United Kingdom
- MR Author ID: 881750
- Email: sisto@maths.ox.ac.uk
- 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
- 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
- MathSciNet review: 3080156