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Introduction to algebraic topology: the fundamental group

Grant number: 11/21268-6
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): February 01, 2012
Effective date (End): December 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Maria Gorete Carreira Andrade
Grantee:Jéssica Cristina Rossinati Rodrigues da Costa
Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil


The present project is an introduction to algebraic topology with the study of some topics in homotopy theory, specifically the study of the fundamental group of a topological space X. Will be seen among other topics: definition, main properties and examples of the fundamental group, the fundamental group as a homotopic invariant, and some examples of calculation of the fundamental group of the union of two spaces. The topics will be developed in a formal way, always looking for a geometric approach, making the student feel the connection between large areas (Algebra and Topology) which we consider very important and beneficial to their training.(AU)

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