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

Mathematics

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

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 3 , proving a conjecture of Smirnov.

Original language	English
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/s0002-9939-2013-11669-2
Publication status	Published - 14 Jun 2013

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title = "Embedding universal covers of graph manifolds in products of trees",

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 3 , proving a conjecture of Smirnov.",

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AB - 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 3 , proving a conjecture of Smirnov.

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Embedding universal covers of graph manifolds in products of trees

Abstract

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