Gaps in the differential forms spectrum on cyclic coverings

dc.creatorAnné, Colette
dc.creatorCarron, Gilles
dc.creatorPost, Olaf
dc.date2007-08-29
dc.date2008-04-18
dc.date.accessioned2026-07-07T09:33:02Z
dc.date.available2026-07-07T09:33:02Z
dc.descriptionWe 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.description35 pages, some minor changes and clarifications
dc.identifierhttps://arxiv.org/abs/0708.3981
dc.identifierhttp://arxiv.org/abs/0708.3981
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158994
dc.subjectDifferential Geometry
dc.titleGaps in the differential forms spectrum on cyclic coverings
dc.typetext

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