Algebraic & Geometric Topology 7 (2007) 1063–1070

DOI: 10.2140/agt.2007.7.1063

arXiv: math.MG/0610391

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.

Keywords

asymptotic dimension, quasi-isometry, curve graph

Mathematical Subject Classification

Primary: 51F99

Secondary: 20F69, 54F45, 57M50

References

Publication

Received: 30 November 2006
Revised: 1 May 2007
Accepted: 29 May 2007
Published: 20 June 2007

Authors