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A note on spaces of asymptotic dimension one

Koji Fujiwara·Kevin Whyte
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Abstract

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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Koji Fujiwara, Kevin Whyte. 2006-11-29. A note on spaces of asymptotic dimension one. https://doi.org/10.2140/agt.2007.7.1063

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