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

Smirnov, A.

doi:10.1090/S1061-0022-2013-01267-2

Quasiisometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees
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by A. Smirnov
Translated by: the author

St. Petersburg Math. J. 24 (2013), 811-821

DOI: https://doi.org/10.1090/S1061-0022-2013-01267-2

Published electronically: July 24, 2013

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Abstract:

In every dimension $n\ge 3$, a class of orthogonal graph-manifolds is introduced. It is proved that the fundamental group of any orthogonal graph-manifold embeds quasiisometrically into a product of $n$ trees. As a consequence, it is shown that the asymptotic dimension and the linearly-controlled asymptotic dimensions of such a group are equal to $n$.

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