Non-Wrapping of Hyperbolic Interval Bundles |
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Authors: | Richard Evans John Holt |
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Affiliation: | (1) University of Auckland, Auckland, New Zealand;(2) Present address: TNS Conversa, Level 1, 7 Falcon St., Parnell, Auckland, New Zealand;(3) Inland Revenue Department, 5-7 Byron Avenue, Takapuna, PO Box 33150, Auckland, 0740, New Zealand |
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Abstract: | We demonstrate a condition on the boundary at infinity of a hyperbolic interval bundle N that guarantees that, for any associated geometric limit, there is a compact core for N which embeds under the covering map. The proof involves an analysis of the geometry of torus cusps in a hyperbolic manifold, and techniques of Anderson, Canary and McCullough [AnCM]. Together with results of Holt–Souto [HS] this shows that the locus of non-local-connectivity of the space of once-punctured torus groups is not dense, and describes a relatively open subset of the boundary of the space of once-punctured torus groups consisting of points of non-self-bumping. Received: April 2006, Revision: May 2007, Accepted: December 2007 |
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Keywords: | Kleinian groups topology of deformation spaces |
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