A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls

Autores
Capitelli, Nicolás Ariel; Minian, Elias Gabriel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove a generalization of a result of Dong and Santos– Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres.
Fil: Capitelli, Nicolás Ariel. 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: 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
Materia
Simplicial Complexes
Combinatorial Manifolds
Alexander Dual
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:11336/18862
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18862
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and ballsCapitelli, Nicolás ArielMinian, Elias GabrielSimplicial ComplexesCombinatorial ManifoldsAlexander Dualhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove a generalization of a result of Dong and Santos– Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres.Fil: Capitelli, Nicolás Ariel. 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: 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"; ArgentinaElsevier Inc2016-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18862Capitelli, Nicolás Ariel; Minian, Elias Gabriel; A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls; Elsevier Inc; Journal of Combinatorial Theory Series A; 138; 2-2016; 155-1740097-3165CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0097316515001284info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcta.2015.10.002info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1403.1291info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:55:58Zoai:ri.conicet.gov.ar:11336/18862instacron: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 09:55:59.116CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
title A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
spellingShingle A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
Capitelli, Nicolás Ariel
Simplicial Complexes
Combinatorial Manifolds
Alexander Dual
title_short A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
title_full A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
title_fullStr A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
title_full_unstemmed A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
title_sort A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls
dc.creator.none.fl_str_mv Capitelli, Nicolás Ariel
Minian, Elias Gabriel
author Capitelli, Nicolás Ariel
author_facet Capitelli, Nicolás Ariel
Minian, Elias Gabriel
author_role author
author2 Minian, Elias Gabriel
author2_role author
dc.subject.none.fl_str_mv Simplicial Complexes
Combinatorial Manifolds
Alexander Dual
topic Simplicial Complexes
Combinatorial Manifolds
Alexander Dual
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 prove a generalization of a result of Dong and Santos– Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres.
Fil: Capitelli, Nicolás Ariel. 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: 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
description We prove a generalization of a result of Dong and Santos– Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres.
publishDate 2016
dc.date.none.fl_str_mv 2016-02
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/11336/18862
Capitelli, Nicolás Ariel; Minian, Elias Gabriel; A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls; Elsevier Inc; Journal of Combinatorial Theory Series A; 138; 2-2016; 155-174
0097-3165
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18862
identifier_str_mv Capitelli, Nicolás Ariel; Minian, Elias Gabriel; A generalization of a result of Dong and Santos–Sturmfels on the Alexander dual of spheres and balls; Elsevier Inc; Journal of Combinatorial Theory Series A; 138; 2-2016; 155-174
0097-3165
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0097316515001284
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcta.2015.10.002
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1403.1291
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 Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
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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