Length bounds on curves arising from tight geodesics
Bowditch, Brian H.. (2007) Length bounds on curves arising from tight geodesics. GEOMETRIC AND FUNCTIONAL ANALYSIS, 17 (4). pp. 1001-1042. ISSN 1016-443XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00039-007-0627-6
Let M be a complete hyperbolic 3-manifold admitting a homotopy equivalence to a compact surface Sigma, such that the cusps of M are in bijective correspondence with the boundary components of Sigma. Suppose we realise a tight geodesic in the curve complex as a sequence of closed geodesics M. There is an upper bound on the lengths of such curves in terms of the lengths of the terminal curves and the topologicial type of Sigma. We give proofs of these and related bounds. Similar bounds have been proven by Minsky using the sophisticated machinery of hierarchies. Such bounds feature in the work of Brock, Canary and Minsky towards the ending lamination conjecture, and can also be used to study the action of the mapping class group on the curve complex.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||GEOMETRIC AND FUNCTIONAL ANALYSIS|
|Publisher:||BIRKHAUSER VERLAG AG|
|Number of Pages:||42|
|Page Range:||pp. 1001-1042|
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