A note on spaces of asymptotic dimension one

Details A note on spaces of asymptotic dimension one A note on spaces of asymptotic dimension one

2006-10-12

arxiv.org/abs/math/0610391v2

Mathematics

Metric Geometry

add Example 0.3, 7 pages

Scientific paper

Let $X$ be a geodesic metric space with $H_1(X)$ uniformly generated. If $X$
has asymptotic dimension one then $X$ is quasi-isometric to an unbounded tree.
As a corollary, we show that the asymptotic dimension of the curve graph of a
compact, oriented surface with genus $g \ge 2$ and one boundary component is at
least two.

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