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dc.contributor.author
Console, S.  
dc.contributor.author
Miatello, Roberto Jorge  
dc.contributor.author
Rossetti, Juan Pablo  
dc.date.available
2023-02-02T11:08:52Z  
dc.date.issued
2010-02  
dc.identifier.citation
Console, S.; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Z2-cohomology and spectral properties of flat manifolds of diagonal type; Elsevier Science; Journal Of Geometry And Physics; 60; 5; 2-2010; 760-781  
dc.identifier.issn
0393-0440  
dc.identifier.uri
http://hdl.handle.net/11336/186569  
dc.description.abstract
We study the cohomology groups with Z2-coefficients for compact flat Riemannian manifolds of diagonal type MΓ = Γ {set minus} Rn by explicit computation of the differentials in the Lyndon-Hochschild-Serre spectral sequence. We obtain expressions for Hj (MΓ, Z2), j = 1, 2 and give an effective criterion for the non-vanishing of the second Stiefel-Whitney class w2 (MΓ). We apply the results to exhibit isospectral pairs with special cohomological properties; for instance, we give isospectral 5-manifolds with different H2 (MΓ, Z2), and isospectral 4-manifolds M, M′ having the same Z2-cohomology where w2 (M) = 0 and w2 (M′) ≠ 0. We compute the Z2-cohomology of all generalized Hantzsche-Wendtn-manifolds for n = 3, 4, 5 and we study H2 and w2 for a large n-dimensional family, Kn, with explicit computation for a subfamily of examples due to Lee and Szczarba.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Elsevier Science  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
BIEBERBACH GROUP  
dc.subject
COHOMOLOGY  
dc.subject
SPECTRAL GEOMETRY  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Z2-cohomology and spectral properties of flat manifolds of diagonal type  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2023-01-31T12:32:21Z  
dc.journal.volume
60  
dc.journal.number
5  
dc.journal.pagination
760-781  
dc.journal.pais
Países Bajos  
dc.journal.ciudad
Amsterdam  
dc.description.fil
Fil: Console, S.. Università di Torino; Italia  
dc.description.fil
Fil: Miatello, Roberto Jorge. 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: Rossetti, Juan Pablo. 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.journal.title
Journal Of Geometry And Physics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.geomphys.2010.01.006  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S039304401000029X