Classes de Stiefel-Whitney

• Ano de defesa: 2019
• Autor(a) principal: Castelo Branco Júnior, José Leôncio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Classes características; Cohomologia; Topologia; Obstrução; Fibrados triviais; Characteristic classes; Cohomology; Topology; Obstruction; Trivial bundles; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/18958

In this work we study the Stiefel-Whitney classes of a real smooth varieties. These classes allow us to identify trivial bundles. The motivation and geometric definition of this object are given by means of the cochain obstruction, later they are presented in the axiomatic way. Assuming the existence and uniqueness of such classes satisfing these axioms, we will see some results as Whitney’s Duality Theorem which relates the classes of the tangent bundle with the normal bundle, and Stiefel’s Theorem that allows us to conclude when a real projective space is parallelizable. Finally, we will see the application of this tool in the study of cobordant manifolds.