Hodge theory on hyperbolic manifolds of infinite volume
| dc.creator | Olbrich, Martin | |
| dc.date | 2000-09-04 | |
| dc.date.accessioned | 2026-07-07T04:37:10Z | |
| dc.date.available | 2026-07-07T04:37:10Z | |
| dc.description | Let $Y=Γ\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $Γ$-invariant currents on the sphere at infinity of $H^n$ with support on the limit set of $Γ$. These spaces are finite-dimensional. The main result identifies the cohomology of $Y$ with a quotient of such spaces. We explain in which sense this result generalizes the classical Hodge theorem for compact quotients. We obtain analogous results for the cohomology groups $H^p(Γ,F)$, where $F$ is a finite-dimensional representation of the full group of orientation preserving isometries of $H^n$. | |
| dc.description | 9 pages, to appear in the Proceedings of "Lie Theory and Its Applications in Physics - Lie III" (World Scientific, 2000) | |
| dc.identifier | https://arxiv.org/abs/math/0009038 | |
| dc.identifier | http://arxiv.org/abs/math/0009038 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59858 | |
| dc.subject | Differential Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 58J, 22E40 | |
| dc.title | Hodge theory on hyperbolic manifolds of infinite volume | |
| dc.type | text |