Simplicial Lusternik–Schnirelmann category

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

ISSN: 0214-1493

Año de publicación: 2019

Volumen: 63

Número: 1

Páginas: 265-293

Tipo: Artículo

DOI: 10.5565/PUBLMAT6311909 DIALNET GOOGLE SCHOLAR lock_openDDD editor

Otras publicaciones en: Publicacions matematiques

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.