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Doctoral Thesis
DOI
10.11606/T.45.2019.tde-25032019-092801
Document
Author
Full name
Max Reinhold Jahnke
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Cordaro, Paulo Domingos (President)
Hoepfner, Gustavo
Jacobowitz, Howard
Jacobsen, Gerardo Alvaro Manuel Mendoza
Silva, Paulo Leandro Dattori da
Title in English
Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
Keywords in English
Cohomology
Hypocomplex
Involutive structures
Left-invariant cohomology
Lie groups
Solvability
Abstract in English
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.
Title in Portuguese
Resolubilidade em grau máximo para estruturas hipocomplexas e a cohomologia de estruturas involutivas invariantes à esquerda em grupos de Lie compactos
Keywords in Portuguese
Cohomologia
Cohomologia invariante à esquerda
Estruturas involutivas
Grupos de Lie
Hipocomplexidade
Resolubilidade
Abstract in Portuguese
Usamos a teoria da espaços duais de Fréchet-Schwartz (DFS) para estabelecer uma condição suficiente para resolubilidade em grau máximo para o complexo associado a estrutuas localmente integráveis hipocomplexas. Como aplicação, provamos que a cohomologia de estruturas hipocomplexas invariantes à esquerda podem ser calculadas usando apenas formas invariantes à esquerda, assim reduzindo o cálculo a um método puramente algébrico. No caso de estruturas invariantes à esquerda, sob certas condições razoáveis, provamos que a cohomologia associada à estrutura pode ser calculada usando apenas formas invariantes à esquerda.
 
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Publishing Date
2019-04-02
 
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