Topology of moduli spaces of free group representations in real reductive groups

Detalhes bibliográficos
Autor(a) principal: Casimiro, Ana
Data de Publicação: 2016
Outros Autores: Florentino, Carlos, Lawton, Sean, Oliveira, André
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/36307
Resumo: This work was partially supported by the projects PTDC/MAT-GEO/0675/2012 and PTDC/MAT/120411/2010, FCT, Portugal. The authors also acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: Geometric structures and Representation varieties" (the GEAR Network). Additionally, the third author was partially supported by the Simons Foundation grant 245642 and the U.S. National Science Foundation grant DMS 1309376, and the fourth author was partially supported by Centro de Matematica da Universidade de Tras-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2011).
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spelling Topology of moduli spaces of free group representations in real reductive groupsCharacter varietiesreal reductive groupsrepresentation varietiesCHARACTER VARIETIES2X2 MATRICES3-MANIFOLDSINVARIANTSSPLITTINGSSURFACEThis work was partially supported by the projects PTDC/MAT-GEO/0675/2012 and PTDC/MAT/120411/2010, FCT, Portugal. The authors also acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: Geometric structures and Representation varieties" (the GEAR Network). Additionally, the third author was partially supported by the Simons Foundation grant 245642 and the U.S. National Science Foundation grant DMS 1309376, and the fourth author was partially supported by Centro de Matematica da Universidade de Tras-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2011).Let G be a real reductive algebraic group with maximal compact subgroup K, and let F-r be a rank r free group. We show that the space of closed orbits in Hom(F-r, G)/G admits a strong deformation retraction to the orbit space Hom(F-r, K)/K. In particular, all such spaces have the same homotopy type. We compute the Poincare polynomials of these spaces for some low rank groups G, such as Sp(4, IR) and U(2, 2). We also compare these real moduli spaces to the real points of the corresponding complex moduli spaces, and describe the geometry of many examples.DM - Departamento de MatemáticaRUNCasimiro, AnaFlorentino, CarlosLawton, SeanOliveira, André2018-05-09T22:03:47Z2016-032016-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article20application/pdfhttp://hdl.handle.net/10362/36307eng0933-7741PURE: 1243603https://doi.org/10.1515/forum-2014-0049info: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:RCAAP2024-03-11T04:19:41Zoai:run.unl.pt:10362/36307Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:30:26.181609Repositório 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 Topology of moduli spaces of free group representations in real reductive groups
title Topology of moduli spaces of free group representations in real reductive groups
spellingShingle Topology of moduli spaces of free group representations in real reductive groups
Casimiro, Ana
Character varieties
real reductive groups
representation varieties
CHARACTER VARIETIES
2X2 MATRICES
3-MANIFOLDS
INVARIANTS
SPLITTINGS
SURFACE
title_short Topology of moduli spaces of free group representations in real reductive groups
title_full Topology of moduli spaces of free group representations in real reductive groups
title_fullStr Topology of moduli spaces of free group representations in real reductive groups
title_full_unstemmed Topology of moduli spaces of free group representations in real reductive groups
title_sort Topology of moduli spaces of free group representations in real reductive groups
author Casimiro, Ana
author_facet Casimiro, Ana
Florentino, Carlos
Lawton, Sean
Oliveira, André
author_role author
author2 Florentino, Carlos
Lawton, Sean
Oliveira, André
author2_role author
author
author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Casimiro, Ana
Florentino, Carlos
Lawton, Sean
Oliveira, André
dc.subject.por.fl_str_mv Character varieties
real reductive groups
representation varieties
CHARACTER VARIETIES
2X2 MATRICES
3-MANIFOLDS
INVARIANTS
SPLITTINGS
SURFACE
topic Character varieties
real reductive groups
representation varieties
CHARACTER VARIETIES
2X2 MATRICES
3-MANIFOLDS
INVARIANTS
SPLITTINGS
SURFACE
description This work was partially supported by the projects PTDC/MAT-GEO/0675/2012 and PTDC/MAT/120411/2010, FCT, Portugal. The authors also acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: Geometric structures and Representation varieties" (the GEAR Network). Additionally, the third author was partially supported by the Simons Foundation grant 245642 and the U.S. National Science Foundation grant DMS 1309376, and the fourth author was partially supported by Centro de Matematica da Universidade de Tras-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2011).
publishDate 2016
dc.date.none.fl_str_mv 2016-03
2016-03-01T00:00:00Z
2018-05-09T22:03:47Z
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 http://hdl.handle.net/10362/36307
url http://hdl.handle.net/10362/36307
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0933-7741
PURE: 1243603
https://doi.org/10.1515/forum-2014-0049
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 20
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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
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