Tight geodesics in the curve complex
Bowditch, B. H. (Brian Hayward), 1961- . (2008) Tight geodesics in the curve complex. Inventiones Mathematicae, Vol.171 (No.2). pp. 281-300. ISSN 0020-9910Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00222-007-0081-y
The curve graph, g, associated to a compact surface Sigma is the 1-skeleton of the curve complex defined by Harvey. Masur and Minsky showed that this graph is hyperbolic and defined the notion of a tight geodesic therein. We prove some finiteness results for such geodesics. For example, we show that a slice of the union of tight geodesics between any pair of points has cardinality bounded purely in terms of the topological type of Sigma. We deduce some consequences for the action of the mapping class group on g. In particular, we show that it satisfies an acylindricity condition, and that the stable lengths of pseudoanosov elements are rational with bounded denominator.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Geodesics (Mathematics), Curves|
|Journal or Publication Title:||Inventiones Mathematicae|
|Number of Pages:||20|
|Page Range:||pp. 281-300|
|Access rights to Published version:||Restricted or Subscription Access|
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