Spectra of lens spaces from 1-norm spectra of congruence lattices

Autores
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
To every n-dimensional lens space L, we associate a congruence lattice L in ℤm, with n=2m - 1 and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on L with the number of lattice elements of a given ||·||1-length in l. As a consequence, we show that two lens spaces are isospectral on functions (respectively, isospectral on p-forms for every p) if and only if the associated congruence lattices are ||·||1-isospectral (respectively, ||·||1-isospectral plus a geometric condition). Using this fact, we give, for every dimension n≥ 5, infinitely many examples of Riemannian manifolds that are isospectral on every level p and are not strongly isospectral.
Fil: Lauret, Emilio Agustin. 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: 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
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
Materia
Spectrum
Lattice
Lens Space
Norm One
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:11336/60238
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/60238
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Spectra of lens spaces from 1-norm spectra of congruence latticesLauret, Emilio AgustinMiatello, Roberto JorgeRossetti, Juan PabloSpectrumLatticeLens SpaceNorm Onehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1To every n-dimensional lens space L, we associate a congruence lattice L in ℤm, with n=2m - 1 and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on L with the number of lattice elements of a given ||·||1-length in l. As a consequence, we show that two lens spaces are isospectral on functions (respectively, isospectral on p-forms for every p) if and only if the associated congruence lattices are ||·||1-isospectral (respectively, ||·||1-isospectral plus a geometric condition). Using this fact, we give, for every dimension n≥ 5, infinitely many examples of Riemannian manifolds that are isospectral on every level p and are not strongly isospectral.Fil: Lauret, Emilio Agustin. 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; ArgentinaFil: 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; ArgentinaFil: 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; ArgentinaOxford University Press2016-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60238Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Spectra of lens spaces from 1-norm spectra of congruence lattices; Oxford University Press; International Mathematics Research Notices; 2016; 4; 1-1-2016; 1054-10891073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2016/4/1054/2450863info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnv159info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.7167info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:24Zoai:ri.conicet.gov.ar:11336/60238instacron: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:34982025-09-29 09:33:24.284CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spectra of lens spaces from 1-norm spectra of congruence lattices
title Spectra of lens spaces from 1-norm spectra of congruence lattices
spellingShingle Spectra of lens spaces from 1-norm spectra of congruence lattices
Lauret, Emilio Agustin
Spectrum
Lattice
Lens Space
Norm One
title_short Spectra of lens spaces from 1-norm spectra of congruence lattices
title_full Spectra of lens spaces from 1-norm spectra of congruence lattices
title_fullStr Spectra of lens spaces from 1-norm spectra of congruence lattices
title_full_unstemmed Spectra of lens spaces from 1-norm spectra of congruence lattices
title_sort Spectra of lens spaces from 1-norm spectra of congruence lattices
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 Spectrum
Lattice
Lens Space
Norm One
topic Spectrum
Lattice
Lens Space
Norm One
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv To every n-dimensional lens space L, we associate a congruence lattice L in ℤm, with n=2m - 1 and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on L with the number of lattice elements of a given ||·||1-length in l. As a consequence, we show that two lens spaces are isospectral on functions (respectively, isospectral on p-forms for every p) if and only if the associated congruence lattices are ||·||1-isospectral (respectively, ||·||1-isospectral plus a geometric condition). Using this fact, we give, for every dimension n≥ 5, infinitely many examples of Riemannian manifolds that are isospectral on every level p and are not strongly isospectral.
Fil: Lauret, Emilio Agustin. 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: 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
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
description To every n-dimensional lens space L, we associate a congruence lattice L in ℤm, with n=2m - 1 and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on L with the number of lattice elements of a given ||·||1-length in l. As a consequence, we show that two lens spaces are isospectral on functions (respectively, isospectral on p-forms for every p) if and only if the associated congruence lattices are ||·||1-isospectral (respectively, ||·||1-isospectral plus a geometric condition). Using this fact, we give, for every dimension n≥ 5, infinitely many examples of Riemannian manifolds that are isospectral on every level p and are not strongly isospectral.
publishDate 2016
dc.date.none.fl_str_mv 2016-01-01
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/11336/60238
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Spectra of lens spaces from 1-norm spectra of congruence lattices; Oxford University Press; International Mathematics Research Notices; 2016; 4; 1-1-2016; 1054-1089
1073-7928
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60238
identifier_str_mv Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Spectra of lens spaces from 1-norm spectra of congruence lattices; Oxford University Press; International Mathematics Research Notices; 2016; 4; 1-1-2016; 1054-1089
1073-7928
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2016/4/1054/2450863
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnv159
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.7167
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/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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 13.070432

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