Introduction to algebraic topology

• Grant number: 14/15885-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2014
• End date: August 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Bianca Barreiro
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The main goal of this project is to give a solid foundation for the student to continue his studies in Fixed Point and Coincidence Theories. In this sense, basic concepts and techniques of Algebraic Topology will be studied. The topics that will be covered are: graphs, homology groups of a simplicial complex, surfaces, relative homology and Eilenberg-Steenrod axioms, graphs on surfaces, topics on singular homology and the Lefschetz-Hopf fixed point Theorem. (AU)