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

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

2012-04-26

arxiv.org/abs/1204.5874v1

Mathematics

Geometric Topology

15 pages

Scientific paper

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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