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| HAL: hal-00293442, version 1 |
| arXiv: 0708.3981 |
| Detailed view |  Export this paper |
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| Mathematische Zeitschrift 262 (2009) 57-90 |
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| Gaps in the differential forms spectrum on cyclic coverings |
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| Colette Anné 1Gilles Carron 1 |
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| (2009) |
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| 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 $\Sigma$ be a hypersurface in $M$ which does not disconnect $M$ and such that $M-\Sigma$ is a fundamental domain of the covering. If the cohomology group $H^{n/2 (\Sigma)$ 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 $H^{n/2}(\Sigma) \ne 0$, the same statement holds true for the Hodge-de Rham operators on $p$-forms provided $p \notin \{n/2,n/2+1\}$. |
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| 1: | Laboratoire de Mathématiques Jean Leray (LMJL) |
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CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes |
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| Subject | : | Mathematics/Differential Geometry |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/0708.3981 |
| hal-00293442, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00293442 | |
| oai:hal.archives-ouvertes.fr:hal-00293442 | |
| From: Colette Anné | |
| Submitted on: Friday, 4 July 2008 15:31:55 | |
| Updated on: Wednesday, 27 June 2012 15:56:37 | |
