Introduction to algebraic topology

• Grant number: 18/18592-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2018
• End date: October 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Leonardo Gimenez Seabra
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 16/24707-4 - Algebraic, geometric and differential topology, AP.TEM

Abstract

The current scientific initiation project has as main goals to develop the student mathematical maturity and scientific interest. The chosen theme to reach this purpose was Algebraic Topology, more precisely Homology Theory, whose importance in Mathematica is notorious. Besides being a well-sophisticated research area, the prerequisite needed for the proposed study was acquired by the student in voluntary scientific initiation projects during his earliest three semesters in college. The final goal of this project is the equivalence between the concepts of Simplicial Homology and Singular Homology. As much as possible, other topics not directly related will be inserted with the intention to show the student the relations of Topology with others areas of Mathematics.