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2007 A note on spaces of asymptotic dimension one
Koji Fujiwara, Kevin Whyte
Algebr. Geom. Topol. 7(2): 1063-1070 (2007). DOI: 10.2140/agt.2007.7.1063

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 g2 and one boundary component is at least two.

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Koji Fujiwara. Kevin Whyte. "A note on spaces of asymptotic dimension one." Algebr. Geom. Topol. 7 (2) 1063 - 1070, 2007. https://doi.org/10.2140/agt.2007.7.1063

Information

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

zbMATH: 1141.51010
MathSciNet: MR2336248
Digital Object Identifier: 10.2140/agt.2007.7.1063

Subjects:
Primary: 51F99
Secondary: 20F69, 54F45, 57M50

Rights: Copyright © 2007 Mathematical Sciences Publishers

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