Simplicial Lusternik–Schnirelmann category

1. Fernandez-Ternero, Desamparados
2. Macías-Virgós, Enrique
3. Minuz, Erica
4. Vilches Alarcón, José Antonio

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DOI: 10.5565/PUBLMAT6311909 DIALNET GOOGLE SCHOLAR lock_openDDD editor

More publications in: Publicacions matematiques

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.

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