Solvable models for Kodaira surfaces

Autores
Console, Sergio; Ovando, Gabriela Paola; Subils, Mauro
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, we study families of compact spaces which are of the form G/Λk,iG/Λk,i for G the oscillator group and Λk,iFil: Console, Sergio. Universita di Torino; Italia
Fil: Ovando, Gabriela Paola. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina
Fil: Subils, Mauro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
Solvmanifolds
Solvable Lie Group
Heisenberg Group
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:11336/13404
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/13404
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Solvable models for Kodaira surfacesConsole, SergioOvando, Gabriela PaolaSubils, MauroSolvmanifoldsSolvable Lie GroupHeisenberg Grouphttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, we study families of compact spaces which are of the form G/Λk,iG/Λk,i for G the oscillator group and Λk,i<GΛk,i<G a lattice. The solvmanifolds G/Λk,iG/Λk,i are not pairwise diffeomorphic and one has the coverings G→Mk,0→Mk,π→Mk,π/2G→Mk,0→Mk,π→Mk,π/2 for k∈Zk∈Z . We compute their cohomologies and minimal models. Each manifold Mk, 0 is diffeomorphic to a Kodaira–Thurston manifold, i.e., a compact quotient S1×H3(R)/ΓkS1×H3(R)/Γk where ΓkΓk is a lattice of the real three-dimensional Heisenberg group H3(R)H3(R) . Furthermore, any Mk, 0 provides an example of a solvmanifold whose cohomology does not depend on the Lie algebra only. We explain some geometrical aspects of those compact spaces, to show how to distinguish them (by invariant complex, symplectic and metric structures). For instance, no invariant symplectic structure of G can be induced to the any quotient.Fil: Console, Sergio. Universita di Torino; ItaliaFil: Ovando, Gabriela Paola. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; ArgentinaFil: Subils, Mauro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaSpringer2015-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13404Console, Sergio; Ovando, Gabriela Paola; Subils, Mauro; Solvable models for Kodaira surfaces; Springer; Mediterranean Journal Of Mathematics; 12; 1; 2-2015; 187-2041660-54461660-5454enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00009-014-0399-9info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00009-014-0399-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:07:56Zoai:ri.conicet.gov.ar:11336/13404instacron: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:34982025-10-15 15:07:57.02CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Solvable models for Kodaira surfaces
title Solvable models for Kodaira surfaces
spellingShingle Solvable models for Kodaira surfaces
Console, Sergio
Solvmanifolds
Solvable Lie Group
Heisenberg Group
title_short Solvable models for Kodaira surfaces
title_full Solvable models for Kodaira surfaces
title_fullStr Solvable models for Kodaira surfaces
title_full_unstemmed Solvable models for Kodaira surfaces
title_sort Solvable models for Kodaira surfaces
dc.creator.none.fl_str_mv Console, Sergio
Ovando, Gabriela Paola
Subils, Mauro
author Console, Sergio
author_facet Console, Sergio
Ovando, Gabriela Paola
Subils, Mauro
author_role author
author2 Ovando, Gabriela Paola
Subils, Mauro
author2_role author
author
dc.subject.none.fl_str_mv Solvmanifolds
Solvable Lie Group
Heisenberg Group
topic Solvmanifolds
Solvable Lie Group
Heisenberg Group
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, we study families of compact spaces which are of the form G/Λk,iG/Λk,i for G the oscillator group and Λk,i<GΛk,i<G a lattice. The solvmanifolds G/Λk,iG/Λk,i are not pairwise diffeomorphic and one has the coverings G→Mk,0→Mk,π→Mk,π/2G→Mk,0→Mk,π→Mk,π/2 for k∈Zk∈Z . We compute their cohomologies and minimal models. Each manifold Mk, 0 is diffeomorphic to a Kodaira–Thurston manifold, i.e., a compact quotient S1×H3(R)/ΓkS1×H3(R)/Γk where ΓkΓk is a lattice of the real three-dimensional Heisenberg group H3(R)H3(R) . Furthermore, any Mk, 0 provides an example of a solvmanifold whose cohomology does not depend on the Lie algebra only. We explain some geometrical aspects of those compact spaces, to show how to distinguish them (by invariant complex, symplectic and metric structures). For instance, no invariant symplectic structure of G can be induced to the any quotient.
Fil: Console, Sergio. Universita di Torino; Italia
Fil: Ovando, Gabriela Paola. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina
Fil: Subils, Mauro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description In this work, we study families of compact spaces which are of the form G/Λk,iG/Λk,i for G the oscillator group and Λk,i<GΛk,i<G a lattice. The solvmanifolds G/Λk,iG/Λk,i are not pairwise diffeomorphic and one has the coverings G→Mk,0→Mk,π→Mk,π/2G→Mk,0→Mk,π→Mk,π/2 for k∈Zk∈Z . We compute their cohomologies and minimal models. Each manifold Mk, 0 is diffeomorphic to a Kodaira–Thurston manifold, i.e., a compact quotient S1×H3(R)/ΓkS1×H3(R)/Γk where ΓkΓk is a lattice of the real three-dimensional Heisenberg group H3(R)H3(R) . Furthermore, any Mk, 0 provides an example of a solvmanifold whose cohomology does not depend on the Lie algebra only. We explain some geometrical aspects of those compact spaces, to show how to distinguish them (by invariant complex, symplectic and metric structures). For instance, no invariant symplectic structure of G can be induced to the any quotient.
publishDate 2015
dc.date.none.fl_str_mv 2015-02
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/11336/13404
Console, Sergio; Ovando, Gabriela Paola; Subils, Mauro; Solvable models for Kodaira surfaces; Springer; Mediterranean Journal Of Mathematics; 12; 1; 2-2015; 187-204
1660-5446
1660-5454
url http://hdl.handle.net/11336/13404
identifier_str_mv Console, Sergio; Ovando, Gabriela Paola; Subils, Mauro; Solvable models for Kodaira surfaces; Springer; Mediterranean Journal Of Mathematics; 12; 1; 2-2015; 187-204
1660-5446
1660-5454
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00009-014-0399-9
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00009-014-0399-9
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.22299

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