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Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds

Miatello, Roberto Jorge et al · Springer · 2011

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Author / responsible party
Miatello, Roberto Jorge et al
Publisher
Springer
Year
2011
ISSN
1027-1054
ISSN
1027-1054
Language
English

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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. 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 Fil: Podestá, Ricardo César. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina

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APA 7

Miatello, R. J. E. A. (2011). Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds. http://hdl.handle.net/11336/190933

MLA

Miatello, Roberto Jorge et al. "Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds." 2011. http://hdl.handle.net/11336/190933.

Chicago

Miatello, Roberto Jorge et al. 2011. "Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds.". http://hdl.handle.net/11336/190933.

Harvard

Miatello, R. J. E. A. 2011, Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds, Springer, available at: http://hdl.handle.net/11336/190933 [Accessed 7 Aug. 2026].

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Title
Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds
Author / contributors
Miatello, Roberto Jorge et al
Publisher
Springer
Publication year
2011
ISSN
1027-1054
ISSN
1027-1054
Language
English

Subjects

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SIGNATURE AND BOUNDARY OPERATOR; ETA SERIES; ETA INVARIANT; COMPACT FLAT MANIFOLD; https://purl.org/becyt/ford/1.1; https://purl.org/becyt/ford/1
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