Geodesic
A note on spaces of asymptotic dimension one
Fujiwara, Koji1 ; Whyte, Kevin2
1Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
2Department of Mathematics, University of Illinois at Chicago, Chicago IL 60607-7045, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1063-1070
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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 g ≥ 2 and one boundary component is at least two.

DOI : 10.2140/agt.2007.7.1063
Keywords: asymptotic dimension, quasi-isometry, curve graph

Fujiwara, Koji  1   ; Whyte, Kevin  2

1 Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
2 Department of Mathematics, University of Illinois at Chicago, Chicago IL 60607-7045, USA 
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Fujiwara, Koji; Whyte, Kevin. A note on spaces of asymptotic dimension one. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1063-1070. doi: 10.2140/agt.2007.7.1063

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