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Merge trees decoradas e TDA
(Universidade Federal de São Carlos, 2023-08-10)
In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...
Detectando fatores de variedade de codimensão um com propriedades de posição geral
(Universidade Federal de São Carlos, 2010-05-18)
This work is an approach to the famous "Product with a Line Problem". It investigates the class of topological spaces whose cartesian product with R is a topological manifold. Such spaces are called "Codimension One Manifold ...
Uma nota sobre o teorema de Borsuk-Ulam
(Universidade Federal de São Carlos, 2011-02-25)
The main objective of this work is to prove that the map B defined on F and taking values in B, where F is the set of all continuous functions from Sn to Rn and B is the set of all nonempty closed subsets of Sn, invariant ...
Grupo de tranças e espaços de configurações
(Universidade Federal de São Carlos, 2007-06-27)
In this work, we study the Artin braid group, B(n), and the confguration spaces (ordered and unordered) of a path connected manifold of dimension ¸ 2. The fundamental group of confguration space (unordered) of IR2 is ...
Uma generalização do teorema de Ljusternik-Schnirelmann.
(Universidade Federal de São Carlos, 2005-08-31)
The purpose of this work is to present a generalized version of the classic Ljusternik-Schnirelmann theorem given by H. Steinlein [16] by using the con- cept of genus (c.f. [20]) of a Hausdor® space M with a mapping f : M ...
Ordinary and twisted K-theory
(Universidade Federal de São Carlos, 2022-03-28)
The main topic of this thesis consists in Ordinary and Twisted Topological K-Theory. We begin by describing generalized cohomology theories through the Eilenberg-Steenrod Axioms, in order to set Ordinary K-Theory in these ...