Singular homology

• Grant number: 13/04571-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2013
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Peres Vieira
• Grantee: Alex Melges Barbosa
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The method of Algebraic Topology consists in describing the geometrical structure of a topological space, associating it an algebraic system, typically a group or sequence of groups. To continuous map between the spaces corresponding homomorphisms between groups associated with them. In this project we will develop the singular homology groups. Also study important applications, such as Brouwer's fixed-point theorem and non-existence of non-zero vector field in spheres of dimension pair. (AU)