Modelos finitos de variedades topológicas de dimensión dos mediante grafos dirigidos

Abstract

In the present we develop a generalization to the concept of beat point, developed by Barmak and Minian for posets, on a binary reflexive structure or digraph. By using the concept of beat point we find the core of a finite topological space. Later we describe the classifier space of a 2-manifold, which is obtained as a simplicial complex associated to a binary reflexive structure. Finally we find some finite models for 2-manifolds by means of a digraph, and we present a way to compute the first homotopy group of a finite binary reflexive structure.