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- Title
Gaps in the differential forms spectrum on cyclic coverings.
- Authors
Colette Anné; Gilles Carron; Olaf Post
- Abstract
Abstract We are interested in the spectrum of the Hodge–de Rham operator on a $${\mathbb{Z}}$$ -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 $${N \in \mathbb{N}}$$ 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 $${p \notin \{n/2, n/2 + 1\}}$$ .
- Subjects
COPYING; DOCUMENTATION; LETTER services; COPYING services
- Publication
Mathematische Zeitschrift, 2009, Vol 262, Issue 1, p57
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-008-0363-0