Embedding universal covers of graph manifolds in products of trees
We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular, we showthat the Assouad-Nagata dimension of the universal cover of any closed graphmanifold is 3, proving a conjecture of Smirnov.
Main Authors: | , |
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Format: | Journal article |
Published: |
American Mathematical Society
2013
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Summary: | We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular, we showthat the Assouad-Nagata dimension of the universal cover of any closed graphmanifold is 3, proving a conjecture of Smirnov. |
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