Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 2 (2007), 1063-1070.
A note on spaces of asymptotic dimension one
Let be a geodesic metric space with uniformly generated. If has asymptotic dimension one then 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 and one boundary component is at least two.
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1063-1070.
Received: 30 November 2006
Revised: 1 May 2007
Accepted: 29 May 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 51F99: None of the above, but in this section
Secondary: 20F69: Asymptotic properties of groups 54F45: Dimension theory [See also 55M10] 57M50: Geometric structures on low-dimensional manifolds
Fujiwara, Koji; Whyte, Kevin. A note on spaces of asymptotic dimension one. Algebr. Geom. Topol. 7 (2007), no. 2, 1063--1070. doi:10.2140/agt.2007.7.1063. https://projecteuclid.org/euclid.agt/1513796713