Differential cohomology on maps of pairs and relative-parallel product

• Ano de defesa: 2021
• Autor(a) principal: Nunez Maldonado, Juan Carlos
• Orientador(a): Ruffino, Fabio Ferrari
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: Cohomologia diferencial; Mapas de pares; Produto relativo-paralelo; K-teoria diferencial; Integração relativa e com suporte (verticalmente) compacto
• Palavras-chave em Inglês: Differential cohomology; Maps of pairs; Differential k-theory; Relative and (vertically)-compactly-supported integration
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/15183

In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. The second one describes some concrete models of differential cohomology endowed with the relative-parallel product, showing that the axioms stated above are not empty. The third topic deals with the construction and the axiomatization of some meaningful versions of the Thom morphism and of the integration map, in which the parallel-relative product is essential. These definitions constitute the main application of this product, and they are at the same time the fundamental motivation that led us to consider it.