Incompressible surfaces, hyperbolic volume, Heegaard genus and homology
| dc.creator | Culler, Marc | |
| dc.creator | DeBlois, Jason | |
| dc.creator | Shalen, Peter B. | |
| dc.date | 2008-07-29 | |
| dc.date | 2009-01-07 | |
| dc.date.accessioned | 2026-07-07T12:25:46Z | |
| dc.date.available | 2026-07-07T12:25:46Z | |
| dc.description | We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of the cup product map in H^2(M;Z_2) has dimension at most 1, then M has volume greater than 3.08. The proofs of these geometric results involve new topological results relating the Heegaard genus of a closed Haken manifold M to the Euler characteristic of the kishkes (i.e guts) of the complement of an incompressible surface in M. | |
| dc.description | 24 pages, some typographical errors have been corrected and a few passages were reworded to improve clarity | |
| dc.identifier | https://arxiv.org/abs/0807.4718 | |
| dc.identifier | http://arxiv.org/abs/0807.4718 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214672 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50 | |
| dc.title | Incompressible surfaces, hyperbolic volume, Heegaard genus and homology | |
| dc.type | text |