(Z_2^k)-manifolds are isospectral on forms

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dc.creatorMiatello, R. J.
dc.creatorPodesta, R. A.
dc.creatorRossetti, J. P.
dc.date2004-08-20
dc.date.accessioned2026-07-07T05:11:26Z
dc.date.available2026-07-07T05:11:26Z
dc.descriptionWe obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, $Δ_f$, acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group Z_2^k, with 0<k<n. This formula implies that any two compact flat manifolds with holonomy group Z_2^k having isospectral lattices of translations are isospectral on forms, that is, with respect to $Δ_f$. As a consequence, we construct a large family of pairwise $Δ_f$-isospectral and nonhomeomorphic n-manifolds of cardinality greater than $2^{(n-1)(n-2)/2}$.
dc.description15 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0408285
dc.identifierhttp://arxiv.org/abs/math/0408285
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72243
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.subject58J53; 57R15; 20H15
dc.title(Z_2^k)-manifolds are isospectral on forms
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