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QUASICONVEXITY OF BANDS IN HYPERBOLIC 3-MANIFOLDS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  01 April 2014

BRIAN H. BOWDITCH
BRIAN H. BOWDITCH*
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
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Abstract

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Let $M$ be a complete hyperbolic 3-manifold homotopy equivalent to a compact surface $\Sigma $. Let $\Phi $ be a proper subsurface of $\Sigma $, whose boundary is sufficiently short in $M$. We show that the union of all Margulis tubes and cusps homotopic into $\Phi $ lifts to a uniformly quasiconvex subset of hyperbolic 3-space.

Keywords

hyperbolic 3-manifoldsurface groupquasiconvexity

MSC classification

Secondary: 57M50: Geometric structures on low-dimensional manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 2 , April 2014 , pp. 167 - 185
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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