Relative differential cohomology

• Ano de defesa: 2017
• Autor(a) principal: Rocha Barriga, 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; Carácteres de Cheeger-Simons; Cohomologia de Deligne; K-teoria diferencial; Mapa de Gysin
• Palavras-chave em Inglês: Differential cohomology; Cheeger-Simons characters; Deligne cohomology; Differential K-theory; Gysin map
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/9574

We briefly review the classical construction of the Cheeger-Simons characters, the Deligne cohomology groups and the differential K-theory groups, which are representatives of the absolute differential refinement of the corresponding cohomology theories. We present the axiomatic framework for the differential refinement of a generic cohomology theory in the absolute case, together with the important results of existence and uniqueness developed by Bunke and Schick. Motivated by the introduction of the relative Cheeger-Simons characters, we propose a suitable set of axioms for the relative differential extension of a cohomology theory, we construct a family of long exact sequences involving the differential groups and we extend to the relative case the results of existence and uniqueness. Furthermore, we generalize the notion of Cheeger-Simons character to any cohomology theory and we extend to the relative case the construction of the integration map.