Lusternik-Schnirelmann category of simplicial complexes and finite spaces

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong equivalences, and it only depends on the simplicial structure rather than its...

Descripción completa

Detalles Bibliográficos
Autores: Fernández Ternero, Desamparados, Macías Virgós, Enrique, Vilches Alarcón, José Antonio
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/49120
Acceso en línea:http://hdl.handle.net/11441/49120
https://doi.org/10.1016/j.topol.2015.08.001
Access Level:acceso abierto
Palabra clave:Simplicial complex
Contiguity class
Strong collapse
Lusternik-Schnirelmann category
Finite topological space
Poset
id ES_f2f8487bf457e4f8a6ebe78ae4d23482
oai_identifier_str oai:idus.us.es:11441/49120
network_acronym_str ES
network_name_str España
repository_id_str
spelling Lusternik-Schnirelmann category of simplicial complexes and finite spacesFernández Ternero, DesamparadosMacías Virgós, EnriqueVilches Alarcón, José AntonioSimplicial complexContiguity classStrong collapseLusternik-Schnirelmann categoryFinite topological spacePosetIn this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong equivalences, and it only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of simplicial geometric category. We prove that the maximum value over the simplicial homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of LS-category are obtained in the setting of finite topological spaces.Plan Andaluz de Investigación, Desarrollo e Innovación (Junta de Andalucía)Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalElsevierGeometría y TopologíaFQM326: Geometría Diferencial y Teoría de LieFQM189: Homotopía Propia2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/49120https://doi.org/10.1016/j.topol.2015.08.001reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésTopology and its Applications, 194, 37-50.FQM-326FQM-189info:eu-repo/grantAgreement/MINECO/MTM2013-41768-P/https://doi.org/10.1016/j.topol.2015.08.001info:eu-repo/semantics/openAccessoai:idus.us.es:11441/491202026-06-17T12:51:07Z
dc.title.none.fl_str_mv Lusternik-Schnirelmann category of simplicial complexes and finite spaces
title Lusternik-Schnirelmann category of simplicial complexes and finite spaces
spellingShingle Lusternik-Schnirelmann category of simplicial complexes and finite spaces
Fernández Ternero, Desamparados
Simplicial complex
Contiguity class
Strong collapse
Lusternik-Schnirelmann category
Finite topological space
Poset
title_short Lusternik-Schnirelmann category of simplicial complexes and finite spaces
title_full Lusternik-Schnirelmann category of simplicial complexes and finite spaces
title_fullStr Lusternik-Schnirelmann category of simplicial complexes and finite spaces
title_full_unstemmed Lusternik-Schnirelmann category of simplicial complexes and finite spaces
title_sort Lusternik-Schnirelmann category of simplicial complexes and finite spaces
dc.creator.none.fl_str_mv Fernández Ternero, Desamparados
Macías Virgós, Enrique
Vilches Alarcón, José Antonio
author Fernández Ternero, Desamparados
author_facet Fernández Ternero, Desamparados
Macías Virgós, Enrique
Vilches Alarcón, José Antonio
author_role author
author2 Macías Virgós, Enrique
Vilches Alarcón, José Antonio
author2_role author
author
dc.contributor.none.fl_str_mv Geometría y Topología
FQM326: Geometría Diferencial y Teoría de Lie
FQM189: Homotopía Propia
dc.subject.none.fl_str_mv Simplicial complex
Contiguity class
Strong collapse
Lusternik-Schnirelmann category
Finite topological space
Poset
topic Simplicial complex
Contiguity class
Strong collapse
Lusternik-Schnirelmann category
Finite topological space
Poset
description In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong equivalences, and it only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of simplicial geometric category. We prove that the maximum value over the simplicial homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of LS-category are obtained in the setting of finite topological spaces.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/49120
https://doi.org/10.1016/j.topol.2015.08.001
url http://hdl.handle.net/11441/49120
https://doi.org/10.1016/j.topol.2015.08.001
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Topology and its Applications, 194, 37-50.
FQM-326
FQM-189
info:eu-repo/grantAgreement/MINECO/MTM2013-41768-P/
https://doi.org/10.1016/j.topol.2015.08.001
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869424332177932288
score 15.300724

Similares en LA Referencia