Sobre invariantes topológicos de folheações holomorfas com singularidade isolada

• Ano de defesa: 2017
• Autor(a) principal: Araujo, Hamilton Regis Menezes de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Invariantes topológicos; Folheações holomorfas; Singularidades; Holomorphic foliations; Topological invariants; Singularities
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/22884

Considering the foliation induced by a complex holomorph vector field, we will look for topological invariants in the neighborhood of a singular point. At first, the Milnor Number of a vector field becomes important, in the sense that this number is topological invariant. In another discussion, we will emphasize vector fields in dimension two, in which case the leaves, whose foliation is induced by the field, will be integral curves of a 1-form. In this sense, we will deal with Desingularization, that is, after a finite number of processes, which we will call Blow-ups or explosions, we will turn the initial foliation into a foliation whose singularities are all simple. Finally, the Desingularization process of a field will give us tools that make it possible to relate the data obtained in this process to the objects treated throughout the work, with this we will present other topological invariants of foliations.