An introduction to the theories of homological algebra and singular homology

• Grant number: 21/00686-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2021
• End date: January 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Thaís Fernanda Mendes Monis
• Grantee: Marina Maria de Miguel
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The main objective of this research project is to initiate the student in scientific research and writing. Initially, we will take as starting point introductory topics of Homological Algebra, since homological functors are recurrent in all Mathematics and it is in Homological Algebra Theory that we investigate the general properties of such functors. Once developed the language of Homological Algebra, we will move on to the particular study of Singular Homology Theory, as well as some of its applications such as Brouwer's fixed point theorem and some results on the degree of applications between spheres. (AU)