A note on coverings of posets, A-spaces and polyhedra

Autores
Barmak, Jonathan Ariel; Minian, Elias Gabriel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. The coverings of a poset can be understood in two equivalent ways, as categorical coverings, when the poset is viewed as a category, or as topological coverings, when it is viewed as an A-space. This implies that the theory of coverings of polyhedra can be handled completely in the combinatorial setting.
Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
A-SPACE
COVERING MAP
POSET
SIMPLICIAL COMPLEX
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:11336/55418
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A note on coverings of posets, A-spaces and polyhedraBarmak, Jonathan ArielMinian, Elias GabrielA-SPACECOVERING MAPPOSETSIMPLICIAL COMPLEXhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. The coverings of a poset can be understood in two equivalent ways, as categorical coverings, when the poset is viewed as a category, or as topological coverings, when it is viewed as an A-space. This implies that the theory of coverings of polyhedra can be handled completely in the combinatorial setting.Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaInternational Press Boston2016-01info: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/11336/55418Barmak, Jonathan Ariel; Minian, Elias Gabriel; A note on coverings of posets, A-spaces and polyhedra; International Press Boston; Homology, Homotopy And Applications (hha); 18; 1; 1-2016; 143-1501532-0073CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://intlpress.com/site/pub/pages/journals/items/hha/content/vols/0018/0001/a008/index.htmlinfo:eu-repo/semantics/altIdentifier/doi/10.4310/HHA.2016.v18.n1.a8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:23:15Zoai:ri.conicet.gov.ar:11336/55418instacron: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:34982025-09-10 13:23:15.726CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on coverings of posets, A-spaces and polyhedra
title A note on coverings of posets, A-spaces and polyhedra
spellingShingle A note on coverings of posets, A-spaces and polyhedra
Barmak, Jonathan Ariel
A-SPACE
COVERING MAP
POSET
SIMPLICIAL COMPLEX
title_short A note on coverings of posets, A-spaces and polyhedra
title_full A note on coverings of posets, A-spaces and polyhedra
title_fullStr A note on coverings of posets, A-spaces and polyhedra
title_full_unstemmed A note on coverings of posets, A-spaces and polyhedra
title_sort A note on coverings of posets, A-spaces and polyhedra
dc.creator.none.fl_str_mv Barmak, Jonathan Ariel
Minian, Elias Gabriel
author Barmak, Jonathan Ariel
author_facet Barmak, Jonathan Ariel
Minian, Elias Gabriel
author_role author
author2 Minian, Elias Gabriel
author2_role author
dc.subject.none.fl_str_mv A-SPACE
COVERING MAP
POSET
SIMPLICIAL COMPLEX
topic A-SPACE
COVERING MAP
POSET
SIMPLICIAL COMPLEX
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 show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. The coverings of a poset can be understood in two equivalent ways, as categorical coverings, when the poset is viewed as a category, or as topological coverings, when it is viewed as an A-space. This implies that the theory of coverings of polyhedra can be handled completely in the combinatorial setting.
Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description We show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. The coverings of a poset can be understood in two equivalent ways, as categorical coverings, when the poset is viewed as a category, or as topological coverings, when it is viewed as an A-space. This implies that the theory of coverings of polyhedra can be handled completely in the combinatorial setting.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
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/11336/55418
Barmak, Jonathan Ariel; Minian, Elias Gabriel; A note on coverings of posets, A-spaces and polyhedra; International Press Boston; Homology, Homotopy And Applications (hha); 18; 1; 1-2016; 143-150
1532-0073
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55418
identifier_str_mv Barmak, Jonathan Ariel; Minian, Elias Gabriel; A note on coverings of posets, A-spaces and polyhedra; International Press Boston; Homology, Homotopy And Applications (hha); 18; 1; 1-2016; 143-150
1532-0073
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://intlpress.com/site/pub/pages/journals/items/hha/content/vols/0018/0001/a008/index.html
info:eu-repo/semantics/altIdentifier/doi/10.4310/HHA.2016.v18.n1.a8
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 International Press Boston
publisher.none.fl_str_mv International Press Boston
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
_version_ 1842981283586637824
score 12.48226

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