Sobre invariantes topológicos de folheações holomorfas com singularidade isolada

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 w...

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Detalles Bibliográficos
Autor: Araujo, Hamilton Regis Menezes de
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/22884
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/22884
Access Level:acceso abierto
Palabra clave:Invariantes topológicos
Folheações holomorfas
Singularidades
Holomorphic foliations
Topological invariants
Singularities
Descripción
Sumario: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.