Open Access
2019 Simplicial Lusternik-Schnirelmann category
Desamparados Fernández-Ternero, Enrique Macías-Virgós, Erica Minuz, José Antonio Vilches
Publ. Mat. 63(1): 265-293 (2019). DOI: 10.5565/PUBLMAT6311909


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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Desamparados Fernández-Ternero. Enrique Macías-Virgós. Erica Minuz. José Antonio Vilches. "Simplicial Lusternik-Schnirelmann category." Publ. Mat. 63 (1) 265 - 293, 2019.


Received: 25 May 2017; Revised: 24 October 2017; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040969
MathSciNet: MR3908794
Digital Object Identifier: 10.5565/PUBLMAT6311909

Primary: 06F30 , 55M30 , 55U10

Keywords: geometric realization , graph arboricity , Lusternik–Schnirelmann category , strong homotopy type , Whitehead formulation of category

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 1 • 2019
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