A note on the homotopy type of the Alexander dual

Autores
Minian, Elias Gabriel; Rodríguez, Jorge Tomás
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of K does not determine the homotopy type of its dual K∗ . We construct for each finitely presented group G, a simply connected simplicial complex K such that π1(K∗ ) = G and study sufficient conditions on K for K∗ to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute.
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Materia
Dualidad Alexander
Complejos Simpliciales
Homologia
Lattice
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:11336/18736
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18736
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A note on the homotopy type of the Alexander dualMinian, Elias GabrielRodríguez, Jorge TomásDualidad AlexanderComplejos SimplicialesHomologiaLatticehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of K does not determine the homotopy type of its dual K∗ . We construct for each finitely presented group G, a simply connected simplicial complex K such that π1(K∗ ) = G and study sufficient conditions on K for K∗ to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute.Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaSpringer2014-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18736Minian, Elias Gabriel; Rodríguez, Jorge Tomás; A note on the homotopy type of the Alexander dual; Springer; Discrete And Computational Geometry; 52; 1; 7-2014; 34-430179-53761432-0444CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-014-9606-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00454-014-9606-5info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1206.3368info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:45:40Zoai:ri.conicet.gov.ar:11336/18736instacron: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:34982025-10-22 11:45:40.828CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on the homotopy type of the Alexander dual
title A note on the homotopy type of the Alexander dual
spellingShingle A note on the homotopy type of the Alexander dual
Minian, Elias Gabriel
Dualidad Alexander
Complejos Simpliciales
Homologia
Lattice
title_short A note on the homotopy type of the Alexander dual
title_full A note on the homotopy type of the Alexander dual
title_fullStr A note on the homotopy type of the Alexander dual
title_full_unstemmed A note on the homotopy type of the Alexander dual
title_sort A note on the homotopy type of the Alexander dual
dc.creator.none.fl_str_mv Minian, Elias Gabriel
Rodríguez, Jorge Tomás
author Minian, Elias Gabriel
author_facet Minian, Elias Gabriel
Rodríguez, Jorge Tomás
author_role author
author2 Rodríguez, Jorge Tomás
author2_role author
dc.subject.none.fl_str_mv Dualidad Alexander
Complejos Simpliciales
Homologia
Lattice
topic Dualidad Alexander
Complejos Simpliciales
Homologia
Lattice
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of K does not determine the homotopy type of its dual K∗ . We construct for each finitely presented group G, a simply connected simplicial complex K such that π1(K∗ ) = G and study sufficient conditions on K for K∗ to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute.
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
description We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of K does not determine the homotopy type of its dual K∗ . We construct for each finitely presented group G, a simply connected simplicial complex K such that π1(K∗ ) = G and study sufficient conditions on K for K∗ to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute.
publishDate 2014
dc.date.none.fl_str_mv 2014-07
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/11336/18736
Minian, Elias Gabriel; Rodríguez, Jorge Tomás; A note on the homotopy type of the Alexander dual; Springer; Discrete And Computational Geometry; 52; 1; 7-2014; 34-43
0179-5376
1432-0444
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18736
identifier_str_mv Minian, Elias Gabriel; Rodríguez, Jorge Tomás; A note on the homotopy type of the Alexander dual; Springer; Discrete And Computational Geometry; 52; 1; 7-2014; 34-43
0179-5376
1432-0444
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-014-9606-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00454-014-9606-5
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1206.3368
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
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 12.982451

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