Embedding universal covers of graph manifolds in products of trees

David Hume; Alessandro Sisto

doi:10.1090/S0002-9939-2013-11669-2

Embedding universal covers of graph manifolds in products of trees

David Hume, Alessandro Sisto

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove that the universal cover of any graph manifold quasiisometrically 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.

Original language	English
Pages (from-to)	3337-3340
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	10
Early online date	14 Jun 2013
DOIs	https://doi.org/10.1090/S0002-9939-2013-11669-2
Publication status	Published - 1 Aug 2013

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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AB - We prove that the universal cover of any graph manifold quasiisometrically 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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Embedding universal covers of graph manifolds in products of trees

Abstract

ASJC Scopus subject areas

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