|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|
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.