Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups

• Ano de defesa: 2018
• Autor(a) principal: Jahnke, Max Reinhold
• 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; Cohomologia invariante à esquerda; Cohomology; Estruturas involutivas; Grupos de Lie; Hipocomplexidade; Hypocomplex; Involutive structures; Left-invariant cohomology; Lie groups; Resolubilidade; Solvability
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/

We use the theory of dual of Fréchet-Schwartz (DFS) spaces to establish a sufficient condition for top-degree solvability for the differential complex associated to a hypocomplex locally integrable structure. As an application, we show that the top-degree cohomology of left-invariant hypocomplex structures on a compact Lie group can be computed only by using left-invariant forms, thus reducing the computation to a purely algebraic one. In the case of left-invariant elliptic involutive structures on compact Lie groups, under certain reasonable conditions, we prove that the cohomology associated to the involutive structure can be computed only by using left-invariant forms.