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Equisingularidades de funções definidas em ICIS e IDS
(Universidade Federal de São Carlos, 2020-03-10)
We study the equisingularity of a family of function germs $\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $\{(X_t,0)\}$ is a family of $d$-dimensional isolated determinantal singularity. We define the $(d-1)$th polar ...
Sobre teoremas do tipo Tverberg
(Universidade Federal de São Carlos, 2020-12-17)
The main objective of this work is to prove Tverberg-type theorems and related results. More specifically, we will present an alternative proof for the Bárány-Larman conjecture for the case $r = p-1 $ with $ p $ a prime, ...
Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos
(Universidade Federal de São Carlos, 2020-12-07)
The link between braid groups on surfaces and crystallographic groups has become such an interesting topic. In the last years some advances were found in the studies of this relation, specially in the case of Artin braid ...
Involuções fixando RP(6)URP(2n) e variedades compatíveis com o ponto com respeito à involuções
(Universidade Federal de São Carlos, 2020-11-25)
In this work, we have two objectives: the first lives in the context of the classification, up to equivariant cobordism, of the pairs (M, T) , where M is a closed and smooth manifold and T is a smooth involution ...
Twisted Borel K-theory and isomorphisms between differential models of K-theory
(Universidade Federal de São Carlos, 2022-07-04)
In this thesis we discuss some topics about twisted K-theory calculations and equivalences between a couple of differential extension models. We start with a mathematical review of models for twisted K-theory, differential ...
Compactly-supported and relative integration in differential cohomology
(Universidade Federal de São Carlos, 2022-04-11)
In this work, we have constructed more general versions of differential integration maps
in differential cohomology theories. Among the obtained versions we can mention the
integration with compact supports, the integration ...
Ações de Z2k com o conjunto de pontos fixos conexo e a propriedade CP
(Universidade Federal de São Carlos, 2021-10-27)
It is well known that if $\phi:G \times M^m \rightarrow M^m$ is a smooth action of a compact Lie group on a closed smooth manifold, then its fixed point set $F_{\phi} = \bigcup\limits_{i=0}^{n}F^{i}$ is a disjoint union ...
Differential cohomology on maps of pairs and relative-parallel product
(Universidade Federal de São Carlos, 2021-10-06)
In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. ...
Classificação de centros Hamiltonianos polinomiais biquadrados, e isocronicidade trivial versus formas canônicas para aplicações polinomiais no plano de Jacobiano unitário
(Universidade Federal de São Carlos, 2022-10-10)
This work, we classify a non- degenerate center at the origin of a planar Hamiltonian system associated to a function of the form $H(x,y)=A(x)+B(x)y^2 + C(x)y^4$, where $A$, $B$ and $C$ are polynomials. After seing a ...
Classes características de variedades topológicas e generalizadas
(Universidade Federal de São Carlos, 2022-03-24)
In this work, we will initially present generalized bundles, a concept developed by Fadell with
the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the
context of smooth manifolds ...