Injectivity Radius Bounds in Hyperbolic Convex Cores I

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

1999-07-09

arxiv.org/abs/math/9907058v1

Mathematics

Geometric Topology

23 pages, 1 figure

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. In previous work, the author has proven the conjecture for $I$-bundles over a closed surface, taking into account the possibility of cusps. In this paper, we establish the conjecture in the case that M is a book of I-bundles or an acylindrical, hyperbolizable 3-manifold. In particular, we show that if M is a book of I-bundles, then the bound on injectivity radius depends on the number of generators in the fundamental group of M.

Affiliated with

Also associated with

No associations

Rating

Injectivity Radius Bounds in Hyperbolic Convex Cores I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Injectivity Radius Bounds in Hyperbolic Convex Cores I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Injectivity Radius Bounds in Hyperbolic Convex Cores I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-9743