On the Betti Numbers of Finite Volume Hyperbolic Manifolds
| dc.contributor.author | Cerbo, Luca F Di | |
| dc.contributor.author | Stern, Mark | |
| dc.date.accessioned | 2021-12-13T20:12:29Z | |
| dc.date.available | 2021-12-13T20:12:29Z | |
| dc.date.updated | 2021-12-13T20:12:28Z | |
| dc.description.abstract | We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application of the techniques of [DS17]. We also provide effective upper bounds for Betti numbers of compact quaternionic- and Cayley-hyperbolic manifolds in most degrees. More importantly, we extend our techniques to complete finite volume real- and complex-hyperbolic manifolds. In this setting, we develop new monotonicity inequalities for strongly harmonic forms on hyperbolic cusps and employ a new peaking argument to estimate $L^2$-cohomology ranks. Finally, we provide bounds on the de Rham cohomology of such spaces, using a combination of our bounds on $L^2$-cohomology, bounds on the number of cusps in terms of the volume, and the topological interpretation of reduced $L^2$-cohomology on certain rank one locally symmetric spaces. | |
| dc.identifier.uri | ||
| dc.subject | math.DG | |
| dc.subject | math.DG | |
| dc.subject | math.GT | |
| dc.title | On the Betti Numbers of Finite Volume Hyperbolic Manifolds | |
| dc.type | Journal article | |
| duke.contributor.orcid | Stern, Mark|0000-0002-6550-5515 | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Duke |