Injectivity Radius Bounds in Hyperbolic IBundle Convex Cores
Abstract
A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3manifold 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 Ibundle over a closed surface, taking into account the possibility of cusps.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:math/9907052
 Bibcode:
 1999math......7052F
 Keywords:

 Geometric Topology;
 57M50 (primary);
 30F40;
 57N10 (Secondary)
 EPrint:
 42 pages, 6 figures