Algebraic & Geometric Topology

A note on spaces of asymptotic dimension one

Koji Fujiwara and Kevin Whyte

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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 g2 and one boundary component is at least two.

Article information

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

Received: 30 November 2006
Revised: 1 May 2007
Accepted: 29 May 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51F99: None of the above, but in this section
Secondary: 20F69: Asymptotic properties of groups 54F45: Dimension theory [See also 55M10] 57M50: Geometric structures on low-dimensional manifolds

asymptotic dimension quasi-isometry curve graph


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.

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