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Topics in Algebraic Topology: The homology groups of a space X.

Grant number: 13/23811-4
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): February 01, 2014
Effective date (End): December 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Maria Gorete Carreira Andrade
Grantee:Bruno Caldeira Carlotti de Souza
Home 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

This 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.