Topics in algebraic topology: the homology groups of a space X

• Grant number: 13/23811-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2014
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Gorete Carreira Andrade
• Grantee: Bruno Caldeira Carlotti de Souza
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

These project deals of the study of two technics for calculating the homology groups of a space X: the singular homology groups and the homology group of a CW-complex, named cellular homology, and their properties. The technics of cellular homology are more geometrics than singular homology for computing the homology groups of a CW- complexe. But, for studying in more depth the cellular homology, it is necessary to study the singular homology. Some applications are presented, such as Brower Fixed-Point Theorem and non-existence of a nonzero vector field on 2n-dimensional sphere.