Groups, Geometry, and Dynamics

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Volume 7, Issue 1, 2013, pp. 109–126
DOI: 10.4171/GGD/178

Published online: 2013-01-31

An upper bound for injectivity radii in convex cores

Brian H. Bowditch[1]

(1) University of Warwick, Coventry, United Kingdom

Let $ N $ be a complete hyperbolic 3-manifold with finitely generated fundamental group, and let $ H $ be its convex core. We show that there is an upper bound on the radius of an embedded hyperbolic ball in $ H $, which depends only on the topology of $ N $. As a consequence, we deduce that limit sets of strongly convergent kleinian groups converge.

Keywords: Hyperbolic 3-manifold, convex core, injectivity radius

Bowditch Brian: An upper bound for injectivity radii in convex cores. Groups Geom. Dyn. 7 (2013), 109-126. doi: 10.4171/GGD/178