O-minimal De Rham cohomology

• Ano de defesa: 2017
• Autor(a) principal: Figueiredo, Rodrigo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Cohomologia de De Rham; De Rham cohomology; Estruturas o-minimais; Fecho pfaffiano; O-minimal manifolds; O-minimal structures; Pfaffian closure; Variedades o-minimais
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-28042019-181150/

The aim of this dissertation lies in establishing an o-minimal de Rham cohomology theory for smooth abstract-definable manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function, by following the classical de Rham cohomology. We can specify the o-minimal cohomology groups and attain some properties as the existence of Mayer-Vietoris sequence and the invariance under smooth abstract-definable diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must, working in a tame context that defines sufficiently many primitives, assume the validity of a statement related to Bröcker\'s problem.