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The asymptotic dimension of a curve graph is finite
Author(s) -
Bell Gregory C.,
Fujiwara Koji
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm090
Subject(s) - mathematics , geodesic , graph , combinatorics , dimension (graph theory) , mathematical analysis , discrete mathematics , pure mathematics
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 a finite asymptotic dimension. It follows then that a curve graph has property A 1 . We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus at most 2.