Volume 7, issue 2 (2007)

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A note on spaces of asymptotic dimension one

Koji Fujiwara and Kevin Whyte

Algebraic & Geometric Topology 7 (2007) 1063–1070

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 2000
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
Koji Fujiwara
Graduate School of Information Sciences
Tohoku University
Sendai 980-8579
Japan
Kevin Whyte
Department of Mathematics
University of Illinois at Chicago
Chicago IL 60607-7045
USA