Simplicial Lusternik–Schnirelmann category

• Autores: Desamparados Fernández Ternero , Enrique Macías-Virgós , Erica Minuz, José Antonio Vilches Alarcón
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 1, 2019, págs. 265-293
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6311909
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• Resumen

  • 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.