Betti numbers and injectivity radii
| dc.creator | Culler, Marc | |
| dc.creator | Shalen, Peter B. | |
| dc.date | 2009-01-30 | |
| dc.date.accessioned | 2026-07-07T12:36:48Z | |
| dc.date.available | 2026-07-07T12:36:48Z | |
| dc.description | We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains no fibroid surface then its maximal injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed, with no topological restrictions, that the maximal injectivity radius exceeds arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The proof combines a result due to Przeworski with techniques developed by the authors in the 1990s. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/0902.0014 | |
| dc.identifier | http://arxiv.org/abs/0902.0014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218216 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50; 57N10 | |
| dc.title | Betti numbers and injectivity radii | |
| dc.type | text |