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

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 catego...

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Guardado en:
Detalles Bibliográficos
Publicado: 2016
Materias:
A-space
Covering map
Poset
Simplicial complex
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15320073_v18_n1_p143_Barmak
http://hdl.handle.net/20.500.12110/paper_15320073_v18_n1_p143_Barmak
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15320073_v18_n1_p143_Barmak
record_format dspace
spelling paper:paper_15320073_v18_n1_p143_Barmak2023-06-08T16:19:52Z A note on coverings of posets, a-spaces and polyhedra A-space Covering map Poset Simplicial complex 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. © 2016, International Press. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15320073_v18_n1_p143_Barmak http://hdl.handle.net/20.500.12110/paper_15320073_v18_n1_p143_Barmak
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A-space
Covering map
Poset
Simplicial complex
spellingShingle A-space
Covering map
Poset
Simplicial complex
A note on coverings of posets, a-spaces and polyhedra
topic_facet A-space
Covering map
Poset
Simplicial complex
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. © 2016, International Press.
title A note on coverings of posets, a-spaces and polyhedra
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 note on coverings of posets, a-spaces and polyhedra
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15320073_v18_n1_p143_Barmak
http://hdl.handle.net/20.500.12110/paper_15320073_v18_n1_p143_Barmak
_version_ 1768545944858525696

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