Strongly isospectral manifolds with nonisomorphic cohomology rings

Autores
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For any n≥7n≥7, k≥3k≥3, we give pairs of compact flat nn-manifolds MM, M′M′ with holonomy groups Zk2Z2k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology rings. Moreover, if nn is even, MM is Kähler while M′M′ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n=24n=24 and k=3k=3 there is a family of eight compact flat manifolds (four of them Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Miatello, Roberto Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Rossetti, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
isospectral
cohomology rings
primitive forms
flat manifolds
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/11346
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Strongly isospectral manifolds with nonisomorphic cohomology ringsLauret, Emilio AgustinMiatello, Roberto JorgeRossetti, Juan Pabloisospectralcohomology ringsprimitive formsflat manifoldshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1For any n≥7n≥7, k≥3k≥3, we give pairs of compact flat nn-manifolds MM, M′M′ with holonomy groups Zk2Z2k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology rings. Moreover, if nn is even, MM is Kähler while M′M′ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n=24n=24 and k=3k=3 there is a family of eight compact flat manifolds (four of them Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifoldsFil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Miatello, Roberto Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Rossetti, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaEuropean Mathematical Society2013-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/11346Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Strongly isospectral manifolds with nonisomorphic cohomology rings; European Mathematical Society; Revista Matematica Iberoamericana; 29; 4; 12-2013; 611-6340213-2230enginfo:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=29&iss=2&rank=8info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/RMI/732info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1103.0249v2.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:17Zoai:ri.conicet.gov.ar:11336/11346instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:07:17.724CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Strongly isospectral manifolds with nonisomorphic cohomology rings
title Strongly isospectral manifolds with nonisomorphic cohomology rings
spellingShingle Strongly isospectral manifolds with nonisomorphic cohomology rings
Lauret, Emilio Agustin
isospectral
cohomology rings
primitive forms
flat manifolds
title_short Strongly isospectral manifolds with nonisomorphic cohomology rings
title_full Strongly isospectral manifolds with nonisomorphic cohomology rings
title_fullStr Strongly isospectral manifolds with nonisomorphic cohomology rings
title_full_unstemmed Strongly isospectral manifolds with nonisomorphic cohomology rings
title_sort Strongly isospectral manifolds with nonisomorphic cohomology rings
dc.creator.none.fl_str_mv Lauret, Emilio Agustin
Miatello, Roberto Jorge
Rossetti, Juan Pablo
author Lauret, Emilio Agustin
author_facet Lauret, Emilio Agustin
Miatello, Roberto Jorge
Rossetti, Juan Pablo
author_role author
author2 Miatello, Roberto Jorge
Rossetti, Juan Pablo
author2_role author
author
dc.subject.none.fl_str_mv isospectral
cohomology rings
primitive forms
flat manifolds
topic isospectral
cohomology rings
primitive forms
flat manifolds
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For any n≥7n≥7, k≥3k≥3, we give pairs of compact flat nn-manifolds MM, M′M′ with holonomy groups Zk2Z2k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology rings. Moreover, if nn is even, MM is Kähler while M′M′ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n=24n=24 and k=3k=3 there is a family of eight compact flat manifolds (four of them Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Miatello, Roberto Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Rossetti, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description For any n≥7n≥7, k≥3k≥3, we give pairs of compact flat nn-manifolds MM, M′M′ with holonomy groups Zk2Z2k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology rings. Moreover, if nn is even, MM is Kähler while M′M′ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n=24n=24 and k=3k=3 there is a family of eight compact flat manifolds (four of them Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds
publishDate 2013
dc.date.none.fl_str_mv 2013-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/11346
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Strongly isospectral manifolds with nonisomorphic cohomology rings; European Mathematical Society; Revista Matematica Iberoamericana; 29; 4; 12-2013; 611-634
0213-2230
url http://hdl.handle.net/11336/11346
identifier_str_mv Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Strongly isospectral manifolds with nonisomorphic cohomology rings; European Mathematical Society; Revista Matematica Iberoamericana; 29; 4; 12-2013; 611-634
0213-2230
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=29&iss=2&rank=8
info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/RMI/732
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1103.0249v2.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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