MACÍAS VIRGÓS , Enrique

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong equivalences, and it only depends on the simplicial structure rather than its geometric realization. In a similar way to...

The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned 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 alge- braic topology...

We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik– Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.