Sobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones

Abstract

The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. It is focused on a detailed description of certain types of simplicial, cubical and cellular complexes, namely flag complexes, Cech complexes, Vietoris-Rips complexes, Witness complexes, Delaunay complexes and Alpha complexes will be considered. Additionally, persistent homology will be introduced as the main tool to extract relevant topological information from data sets via the above mentioned kinds of complexes.