descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 20 Jun 2007Embargo end date: 01 Jan 2006 English Publisher:Mathematical Sciences PublishersJournal:Algebraic & Geometric Topology, volume 7, pages 1,063-1,070 (issn: 1472-2747, eissn: 1472-2739,

Authors: Fujiwara, Koji; Whyte, Kevin;

doi: 10.2140/agt.2007.7.1063 , 10.48550/arxiv.math/0610391

arXiv: http://arxiv.org/abs/math/0610391

A note on spaces of asymptotic dimension one

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Abstract

Let $X$ be a geodesic metric space with $H_1(X)$ 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 $g \ge 2$ and one boundary component is at least two.

add Example 0.3, 7 pages

Related Organizations

University of Illinois at Chicago
United States
Tohoku University
Japan
University of Chicago
United States

Keywords

asymptotic dimension, 20F69, Metric Geometry (math.MG), Geometric Topology (math.GT), Group Theory (math.GR), 54F45, 57M50, quasi-isometry, Mathematics - Geometric Topology, 51F99, Mathematics - Metric Geometry, FOS: Mathematics, curve graph, Mathematics - Group Theory

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