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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/18736
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:15:29Zoai: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:34982025-09-29 10:15:29.914CONICET 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/ |
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application/pdf application/pdf application/pdf |
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Springer |
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Springer |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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