Injectivity Radius Bounds in Hyperbolic I-Bundle Convex Cores

Details Injectivity Radius Bounds in Hyperbolic I-Bundle Convex Cores Injectivity Radius Bounds in Hyperbolic I-Bundle Convex Cores

1999-07-08

arxiv.org/abs/math/9907052v1

Mathematics

Geometric Topology

42 pages, 6 figures

Scientific paper

A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the injectivity radius based at points in the convex core of N is bounded above by K. This conjecture suggests that convex cores are uniformly congested. We will give a proof in the case when M is an I-bundle over a closed surface, taking into account the possibility of cusps.

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