| Grant number: | 13/04570-6 |
| Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
| Effective date (Start): | May 01, 2013 |
| Effective date (End): | April 30, 2014 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | João Peres Vieira |
| Grantee: | Taís Roberta Ribeiro |
| 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 is to investigate the structure of a topological space through paths in space. More precisely, given a topological space $ X $ and $ x_0 $ a point of $ X $, associate through closed paths in $ X $ a group denoted by $ \ pi_1 (X, x_0) $ or $ \ pi_1 (X) $ (when space is pathwise connected) called the fundamental group of $ X $. Using such a group, some problems on topological spaces and continuous map can be reduced to purely algebraic problems about groups and homomorphisms. Also, we will study important applications, such as Brouwer's fixed point theorem and Borsuk-Ulam's theorem. (AU) | |
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