21828 articles – 15613 references  [version française]
 HAL: hal-00293442, version 1
 arXiv: 0708.3981
 Mathematische Zeitschrift 262 (2009) 57-90
 Gaps in the differential forms spectrum on cyclic coverings
 (2009)
 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 $p \notin \{n/2,n/2+1\}$.
 1: Laboratoire de Mathématiques Jean Leray (LMJL) CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes
 Subject : Mathematics/Differential Geometry