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

Detalhes bibliográficos
Autor(a) principal: Jahnke, Max Reinhold
Data de Publicação: 2018
Tipo de documento: Tese
Idioma: eng
Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
Texto Completo: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/
Resumo: 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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spelling Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groupsResolubilidade em grau máximo para estruturas hipocomplexas e a cohomologia de estruturas involutivas invariantes à esquerda em grupos de Lie compactosCohomologiaCohomologia invariante à esquerdaCohomologyEstruturas involutivasGrupos de LieHipocomplexidadeHypocomplexInvolutive structuresLeft-invariant cohomologyLie groupsResolubilidadeSolvabilityWe 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.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.Biblioteca Digitais de Teses e Dissertações da USPCordaro, Paulo DomingosJahnke, Max Reinhold2018-12-21info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttp://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2019-04-10T00:06:19Zoai:teses.usp.br:tde-25032019-092801Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212019-04-10T00:06:19Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false
dc.title.none.fl_str_mv Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
Resolubilidade em grau máximo para estruturas hipocomplexas e a cohomologia de estruturas involutivas invariantes à esquerda em grupos de Lie compactos
title Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
spellingShingle Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
Jahnke, Max Reinhold
Cohomologia
Cohomologia invariante à esquerda
Cohomology
Estruturas involutivas
Grupos de Lie
Hipocomplexidade
Hypocomplex
Involutive structures
Left-invariant cohomology
Lie groups
Resolubilidade
Solvability
title_short Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
title_full Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
title_fullStr Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
title_full_unstemmed Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
title_sort Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups
author Jahnke, Max Reinhold
author_facet Jahnke, Max Reinhold
author_role author
dc.contributor.none.fl_str_mv Cordaro, Paulo Domingos
dc.contributor.author.fl_str_mv Jahnke, Max Reinhold
dc.subject.por.fl_str_mv Cohomologia
Cohomologia invariante à esquerda
Cohomology
Estruturas involutivas
Grupos de Lie
Hipocomplexidade
Hypocomplex
Involutive structures
Left-invariant cohomology
Lie groups
Resolubilidade
Solvability
topic Cohomologia
Cohomologia invariante à esquerda
Cohomology
Estruturas involutivas
Grupos de Lie
Hipocomplexidade
Hypocomplex
Involutive structures
Left-invariant cohomology
Lie groups
Resolubilidade
Solvability
description 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.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-21
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/
url http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv
dc.rights.driver.fl_str_mv Liberar o conteúdo para acesso público.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Liberar o conteúdo para acesso público.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.none.fl_str_mv
dc.publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
dc.source.none.fl_str_mv
reponame:Biblioteca Digital de Teses e Dissertações da USP
instname:Universidade de São Paulo (USP)
instacron:USP
instname_str Universidade de São Paulo (USP)
instacron_str USP
institution USP
reponame_str Biblioteca Digital de Teses e Dissertações da USP
collection Biblioteca Digital de Teses e Dissertações da USP
repository.name.fl_str_mv Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)
repository.mail.fl_str_mv virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br
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