Injectivity Radius Bounds in Hyperbolic Convex Cores I
| dc.creator | Fan, Carol E. | |
| dc.date | 1999-07-09 | |
| dc.date.accessioned | 2026-07-07T05:29:51Z | |
| dc.date.available | 2026-07-07T05:29:51Z | |
| dc.description | 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. | |
| dc.description | 23 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/9907058 | |
| dc.identifier | http://arxiv.org/abs/math/9907058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78798 | |
| dc.subject | Geometric Topology | |
| dc.subject | General Topology | |
| dc.subject | 57M50 (Primary); 30F40, 57N10 (Secondary) | |
| dc.title | Injectivity Radius Bounds in Hyperbolic Convex Cores I | |
| dc.type | text |