Volume and topology of bounded and closed hyperbolic 3-manifolds
| dc.creator | DeBlois, Jason | |
| dc.creator | Shalen, Peter B. | |
| dc.date | 2009-02-03 | |
| dc.date.accessioned | 2026-07-07T12:37:21Z | |
| dc.date.available | 2026-07-07T12:37:21Z | |
| dc.description | Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89. The proof of this result uses the following dichotomy: either N has a long return path (defined by Kojima-Miyamoto), or N has an embedded, codimension-0 submanifold X with incompressible boundary $T \sqcup \partial N$, where T is the frontier of X in N, which is not a book of I-bundles. As an application of this result, we show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 5, and if the image in H^2(M;Z_2) of the cup product map has image of dimension at most 1, then M has volume greater than 3.44. | |
| dc.description | 38 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0902.0576 | |
| dc.identifier | http://arxiv.org/abs/0902.0576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218410 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50 | |
| dc.title | Volume and topology of bounded and closed hyperbolic 3-manifolds | |
| dc.type | text |