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dc.contributor.author
Miatello, Roberto Jorge
dc.contributor.author
Podestá, Ricardo César
dc.date.available
2023-03-17T16:37:35Z
dc.date.issued
2011-05
dc.identifier.citation
Miatello, Roberto Jorge; Podestá, Ricardo César; Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds; Springer; The Journal Of Geometric Analysis; 22; 4; 5-2011; 1027-1054
dc.identifier.issn
1050-6926
dc.identifier.uri
http://hdl.handle.net/11336/190933
dc.description.abstract
We study the spectral theory of the Dirac-type boundary operator D defined by Atiyah, Patodi, and Singer, acting on smooth even forms of a compact flat Riemannian manifold M. We give an explicit formula for the multiplicities of the eigenvalues of D in terms of values of characters of exterior representations of SO(n), where n = dim M. As a consequence, we give large families of D-isospectral flat manifolds that are non-homeomorphic to each other. Furthermore, we derive expressions for the eta series in terms of special values of Hurwitz zeta functions and, as a result, we obtain a simple explicit expression of the eta invariant. © Mathematica Josephina, Inc. 2011.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
SIGNATURE AND BOUNDARY OPERATOR
dc.subject
ETA SERIES
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ETA INVARIANT
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COMPACT FLAT MANIFOLD
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-03-15T20:34:19Z
dc.identifier.eissn
1559-002X
dc.journal.volume
22
dc.journal.number
4
dc.journal.pagination
1027-1054
dc.journal.pais
Alemania
dc.description.fil
Fil: Miatello, Roberto Jorge. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.description.fil
Fil: Podestá, Ricardo César. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.journal.title
The Journal Of Geometric Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s12220-011-9227-7
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s12220-011-9227-7
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