Gaps in the differential forms spectrum on cyclic coverings
| dc.creator | Anné, Colette | |
| dc.creator | Carron, Gilles | |
| dc.creator | Post, Olaf | |
| dc.date | 2007-08-29 | |
| dc.date | 2008-04-18 | |
| dc.date.accessioned | 2026-07-07T09:33:02Z | |
| dc.date.available | 2026-07-07T09:33:02Z | |
| dc.description | We are interested in the spectrum of the Hodge-de Rham operator on a cyclic covering $X$ over a compact manifold $M$ of dimension $n+1$. Let $Σ$ be a hypersurface in $M$ which does not disconnect $M$ and such that $M-Σ$ is a fundamental domain of the covering. If the cohomology group $H^{n/2 (Σ)$ is trivial, we can construct for each $N \in \N$ a metric $g=g_N$ on $M$, such that the Hodge-de Rham operator on the covering $(X,g)$ has at least $N$ gaps in its (essential) spectrum. If $H^{n/2}(Σ) \ne 0$, the same statement holds true for the Hodge-de Rham operators on $p$-forms provided $p \notin \{n/2,n/2+1\}$. | |
| dc.description | 35 pages, some minor changes and clarifications | |
| dc.identifier | https://arxiv.org/abs/0708.3981 | |
| dc.identifier | http://arxiv.org/abs/0708.3981 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158994 | |
| dc.subject | Differential Geometry | |
| dc.title | Gaps in the differential forms spectrum on cyclic coverings | |
| dc.type | text |