João Peres Vieira

• Abstract

  Let $T$ be the torus and let $T\to M\stackrel{p}{\to}S^{1}$ be a torus bundle over $S^{1}$. In this work we intend to study the following question: given a pair of fiber preserving maps over $S^1$ when can it be deformed by a fiberwisehomotopy over $S^1$ into a pair of coincidence free fiber preserving maps over $S^1$? Answering this question is equivalent to study existence of a section …

  Coincidence of maps on torus bundle over the circle, AP.R

• Abstract

  The method of Algebraic Topology consists of describing the geometric structure of a topological space, associating to it an algebraic system, usually a group or a sequence of groups. To the continuous functions between spaces correspond homomorphisms between the groups associated to them. In this project we will develop the fundamental group. We will see, for example, that the fundamenta…

  Fundamental group, BP.IC

• 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 topolog…

  Fundamental group, BP.IC

• Abstract

  The method of Algebraic Topology consists in describing the geometrical structure of a topological space, associating it an algebraic system, typically a group or sequence of groups. To continuous map between the spaces corresponding homomorphisms between groups associated with them. In this project we will develop the singular homology groups. Also study important applications, such as B…

  Singular homology, BP.IC

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