Advanced search
Start date

Fundamental group

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


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)

News published in Agência FAPESP Newsletter about the scholarship:
Articles published in other media outlets (0 total):
More itemsLess items

Please report errors in scientific publications list by writing to: