Simplicial Lusternik-Schnirelmann category

The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many not...

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Detalles Bibliográficos
Autores: Fernández Ternero, Desamparados, Macías Virgós, Enrique, Minuz, Erica, Vilches Alarcón, José Antonio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/106288
Acceso en línea:https://hdl.handle.net/11441/106288
https://doi.org/10.5565/PUBLMAT6311909
Access Level:acceso abierto
Palabra clave:Lusternik{Schnirelmann category
strong homotopy type
geometric realization
Whitehead formulation of category
graph arboricity
Descripción
Sumario:The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many notions and results of alge- braic topology which are costumary in the classical theory of Lusternik{Schnirelmann category. Also we compare the simplicial category of a complex with the LS-category of its geometric realization and we discuss the simplicial analogue of the Whitehead formulation of the LS-category.