Obstruction theory, characteristic classes and applications

• Ano de defesa: 2022
• Autor(a) principal: Martins, Edmundo Bernardo de Castro
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bundles; Characteristic classes; Classes características; Fibrados; Homotopia; Homotopy; Local Euler obstruction; Obstrução local de Euler; Obstruction theory; Teoria de obstrução
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-13022023-152723/

The goal of this work is to study and prove some of the main results of Obstruction Theory, as well as to present some possible applications. The proof of these results depends on the development of several prerequisites along the way, like the notions of free and pointed homotopy, H-groups and H-cogroups, homotopy groups and locally trivial bundles. This development culminates in the proof that the problem of extending maps and sections over the skeletons of a CW-complex is controlled by a cohomological invariant. This result is then used to construct the characteristic classes associated with a vector bundle, and also to define the local Euler obstruction of a point in a singular space.