Simplicial Lusternik-Schnirelmann category

The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined 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...

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Detalles Bibliográficos
Autores: Fernandez-Ternero, Desamparados, Macías-Virgós, Enrique, Minuz, Erica, Vilches Alarcón, José Antonio
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:200752
Acceso en línea:https://ddd.uab.cat/record/200752
https://dx.doi.org/urn:doi: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 finite abstract simplicial complex is a new invariant of the strong homotopy type, defined 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 algebraic 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.