REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP

Detalhes bibliográficos
Autor(a) principal: Oliveira, AG
Data de Publicação: 2011
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/10216/86741
Resumo: Given a closed, oriented surface X of genus g >= 2, and a semisimple Lie group G, let R-G be the moduli space of reductive representations of pi(1) X in G. We determine the number of connected components of R-PGL(n,R- R), for n >= 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R-SL(3,R-R) is homotopically equivalent to R-SO(3).
id RCAP_6126e77cb8fbfa9cb9d75dc51e773057
oai_identifier_str oai:repositorio-aberto.up.pt:10216/86741
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUPMatemáticaMathematicsGiven a closed, oriented surface X of genus g >= 2, and a semisimple Lie group G, let R-G be the moduli space of reductive representations of pi(1) X in G. We determine the number of connected components of R-PGL(n,R- R), for n >= 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R-SL(3,R-R) is homotopically equivalent to R-SO(3).20112011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/86741eng0129-167X10.1142/s0129167x11006787Oliveira, AGinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T15:43:00Zoai:repositorio-aberto.up.pt:10216/86741Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:30:20.120916Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
title REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
spellingShingle REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
Oliveira, AG
Matemática
Mathematics
title_short REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
title_full REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
title_fullStr REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
title_full_unstemmed REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
title_sort REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP
author Oliveira, AG
author_facet Oliveira, AG
author_role author
dc.contributor.author.fl_str_mv Oliveira, AG
dc.subject.por.fl_str_mv Matemática
Mathematics
topic Matemática
Mathematics
description Given a closed, oriented surface X of genus g >= 2, and a semisimple Lie group G, let R-G be the moduli space of reductive representations of pi(1) X in G. We determine the number of connected components of R-PGL(n,R- R), for n >= 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R-SL(3,R-R) is homotopically equivalent to R-SO(3).
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10216/86741
url https://hdl.handle.net/10216/86741
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0129-167X
10.1142/s0129167x11006787
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799136213341306880

Registros relacionados