Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
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 str...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-25032019-092801 |
| Acceso en línea: | http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/ |
| Access Level: | acceso abierto |
| Palabra clave: | Cohomologia Cohomologia invariante à esquerda Cohomology Estruturas involutivas Grupos de Lie Hipocomplexidade Hypocomplex Involutive structures Left-invariant cohomology Lie groups Resolubilidade Solvability |
| Sumario: | 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. |
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