Quasi-isometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees

Alexander Smirnov

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arXiv · 1204.5874

Quasi-isometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees

Alexander Smirnov

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Abstract

In every dimension $n\ge 3$ we introduce a class of orthogonal graph-manifolds and prove that the fundamental group of any orthogonal graph-manifold quasi-isometrically embeds into a product of $n$ trees. As a consequence, we obtain that asymptotic and linearly-controlled asymptotic dimensions of such group are equal to $n$.

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Alexander Smirnov. 2012-04-26. Quasi-isometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees. https://arxiv.org/abs/1204.5874

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