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Aspectos homológicos e homotópicos do teorema de Borsuk-Ulam
(Universidade Federal de São Carlos, 2011-02-20)
The objetive of this work is to generalize the classic Borsuk-Ulam's Theorem.
We studied there generalizations with respect to any comapact and Hausdor T-
space. We used in the proofs the Z2-index of Yang and the B-index. ...
Invariantes de singularidades em característica positiva
(Universidade Federal de São Carlos, 2020-03-30)
This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}.
Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...
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 ...
Superfícies mínimas e a teoria min-max de Almgren--Pitts
(Universidade Federal de São Carlos, 2019-08-07)
First, we introduce the basic concept of minimal surfaces and develop some results in the general theory of minimal surfaces.
In the second part, we are interested in the Simon-Smith Min-Max approach to prove the existence ...
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 ...
Problemas elípticos superlineares com ressonância
(Universidade Federal de São Carlos, 2015-08-14)
The aim of this work is to present results about the existence of non-trivial solutions for some classes of resonant and superlinear eliptic systems employing topological methods. More specifcally, we use a-priori bounds ...
A transformação vetorial de Ribaucour para subvariedades de curvatura constante
(Universidade Federal de São Carlos, 2015-06-09)
In this work we obtain a reduction of the vectorial Ribaucour transformation
that preserves the class of submanifolds with constant sectional curvature of space forms.
As a consequence, a process is derived to generate ...
Imersões isométricas de formas espaciais em Sn x R e Hn x R
(Universidade Federal de São Carlos, 2015-06-08)
In this thesis we classify the isometric immersions f : Mm ^ Sm+p x R with m > 3 P < m — ^d c < 1, where Mm denotes a Riemannian manifold with constant sectional curvature equal to c. We obtain partial results on the ...