## Algebraic & Geometric Topology

### A note on spaces of asymptotic dimension one

#### Abstract

Let $X$ be a geodesic metric space with $H1(X)$ 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 $g≥2$ and one boundary component is at least two.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1063-1070.

Dates
Revised: 1 May 2007
Accepted: 29 May 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796713

Digital Object Identifier
doi:10.2140/agt.2007.7.1063

Mathematical Reviews number (MathSciNet)
MR2336248

Zentralblatt MATH identifier
1141.51010

#### Citation

Fujiwara, Koji; Whyte, Kevin. A note on spaces of asymptotic dimension one. Algebr. Geom. Topol. 7 (2007), no. 2, 1063--1070. doi:10.2140/agt.2007.7.1063. https://projecteuclid.org/euclid.agt/1513796713

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