Some results and algorithms on matroids, simplicial complexes and alexandroff spaces

Resumo

THE NEED FOR DATA ANALYSIS HAS GROWN EXPONENTIALLY IN ALL THE SCIENTIFIC FIELDS IN THE TWO LAST DECADE, BECAUSE OF THE BASICS OF THE USE OF COMPUTERS AND THE EXISTENCE IN THE LABORATORIES OF SCIENTIFIC MATERIAL BECOME MORE POWERFUL. BUT NOT ONLY IS THAT A GREAT ABUNDANCE OF DATA BUT THE TOPOLOGY OF THEM HAS BEEN EXTENDED. ALGREBRATIC TOPOLOGY CAN HELP ENORMOUSLY IN THE ANALYSIS OF THIS DATA. THE PIONEERS HAVE FOUNDED A GREAT COMPANY (AYASDI) AND EVERY DAY THERE US MORE INTERESTED TOPOLOGISTS IN THE THEME.In this work we will prove several new results on matroids, simplicial complexes and Alexandroff spaces, most related with the notion of collapsibility. Our last objetive is to study the notion of P-dominated points in an Alexandroff space as a generalization of beat points. Also we will try design useful algorithms to make easier study of the collapsibility of a simplicial complex