Simplicial Lusternik-Schnirelmann category
Fernandez-Ternero, Desamparados (Universidad de Sevilla. Departamento de Geometría y Topología)
Macías-Virgós, Enrique (Universidade de Santiago de Compostela. Departamento de Matemáticas)
Minuz, Erica (Aarhus University (Dinamarca). Department of Mathematics)
Vilches Alarcón, José Antonio (Universidad de Sevilla. Departamento de Geometría y Topología)

Date:	2019
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Lusternik-schnirelmann category ; Strong homotopy type ; Geometric realization ; Whitehead formulation of category ; Graph arboricity
Published in:	Publicacions matemàtiques, Vol. 63 Núm. 1 (2019) , p. 265-293 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/347138
DOI: 10.5565/PUBLMAT6311909

29 p, 508.5 KB

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