Obstruction theory, characteristic classes and applications

• Autor(a) principal: Martins, Edmundo Bernardo de Castro
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-13022023-152723/
• topic: Bundles; Characteristic classes; Classes características; Fibrados; Homotopia; Homotopy; Local Euler obstruction; Obstrução local de Euler; Obstruction theory; Teoria de obstrução

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.