Classes características de variedades topológicas e generalizadas

• Autor(a) principal: Barbosa, Alex Melges
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/16060
• topic: Classes características; Fibrados generalizados; Variedades topológicas; Variedades generalizadas; Fórmula de Wu; Characteristic classes; Generalized bundles; Topological manifolds; Generalized manifolds; Wu’s formula; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA

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 to topological manifolds. After that, we will use the generalized bundles to obtain original results of Thom, Stiefel-Whitney,Wu and Euler classes of topological manifolds, as well as present a second proof of Wu’s formula for topological manifolds and the topological version of the Poincaré-Hopf theorem. Finally, we will use the Poincaré and Poincaré-Lefschetz dualities to more comprehensively construct the Stiefel-Whitney classes of generalized manifolds in order to present, for the first time in the literature, a proof of the Wu’s formula for such manifolds.