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.
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Received: April 2006, Revision: May 2007, Accepted: December 2007
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Evans, R., Holt, J. Non-Wrapping of Hyperbolic Interval Bundles. GAFA Geom. funct. anal. 18, 98–119 (2008). https://doi.org/10.1007/s00039-008-0653-z
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DOI: https://doi.org/10.1007/s00039-008-0653-z