Bowditch, B. H. (Brian Hayward), 1961- . (2008) Tight geodesics in the curve complex. Inventiones Mathematicae, Vol.171 (No.2). pp. 281-300. ISSN 0020-9910

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Abstract

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
Publisher:	Springer
ISSN:	0020-9910
Date:	February 2008
Volume:	Vol.171
Number:	No.2
Number of Pages:	20
Page Range:	pp. 281-300
Identification Number:	10.1007/s00222-007-0081-y
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/30758

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