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Introduction to algebraic topology

Grant number: 18/18592-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): November 01, 2018
Effective date (End): October 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Alexandre Paiva Barreto
Grantee:Leonardo Gimenez Seabra
Home 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.

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