The asymptotic dimension of a curve graph is finite
Abstract
We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve graph of a compact orientable surface. We use this to conclude that a curve graph has finite asymptotic dimension. It follows then that a curve graph has property . We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus .
Keywords
Cite
@article{arxiv.math/0509216,
title = {The asymptotic dimension of a curve graph is finite},
author = {Gregory Bell and Koji Fujiwara},
journal= {arXiv preprint arXiv:math/0509216},
year = {2014}
}
Comments
19 pages. Made some minor revisions. The section on mapping class groups has been rewritten; in particular we compute the asdim of Mod(S) where S has genus at most 2. The last section on open questions has been modified to reflect recent developments. References have been updated