Connected components of Isom(H3)-representations of non-orientable surfaces

Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. The properties of the 'square map' and other related maps s...

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Autor: Duran Batalla, Juan Luis|||0000-0002-6558-3046
Tipo de documento: artigo
Data de publicação:2022
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:258269
Acesso em linha:https://ddd.uab.cat/record/258269
https://dx.doi.org/urn:doi:10.1007/s10711-022-00682-x
Access Level:Acceso aberto
Palavra-chave:Representation varieties
Stiefel-Whitney class
Orientation reversing isometries of H3
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spelling Connected components of Isom(H3)-representations of non-orientable surfacesDuran Batalla, Juan Luis|||0000-0002-6558-3046Representation varietiesStiefel-Whitney classOrientation reversing isometries of H3Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. The properties of the 'square map' and other related maps serve as a technical step towards the counting of the connected components of the variety of representations of π(N) in Isom(H). We show that the variety of representations hom(π(N), Isom (H)) has 2 connected components, which are distinguished by the Stiefel-Whitney classes of the associated flat bundle. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/258269https://dx.doi.org/urn:doi:10.1007/s10711-022-00682-xreponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 BES-2016-079278Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2582692026-06-06T12:50:31Z
dc.title.none.fl_str_mv Connected components of Isom(H3)-representations of non-orientable surfaces
title Connected components of Isom(H3)-representations of non-orientable surfaces
spellingShingle Connected components of Isom(H3)-representations of non-orientable surfaces
Duran Batalla, Juan Luis|||0000-0002-6558-3046
Representation varieties
Stiefel-Whitney class
Orientation reversing isometries of H3
title_short Connected components of Isom(H3)-representations of non-orientable surfaces
title_full Connected components of Isom(H3)-representations of non-orientable surfaces
title_fullStr Connected components of Isom(H3)-representations of non-orientable surfaces
title_full_unstemmed Connected components of Isom(H3)-representations of non-orientable surfaces
title_sort Connected components of Isom(H3)-representations of non-orientable surfaces
dc.creator.none.fl_str_mv Duran Batalla, Juan Luis|||0000-0002-6558-3046
author Duran Batalla, Juan Luis|||0000-0002-6558-3046
author_facet Duran Batalla, Juan Luis|||0000-0002-6558-3046
author_role author
dc.subject.none.fl_str_mv Representation varieties
Stiefel-Whitney class
Orientation reversing isometries of H3
topic Representation varieties
Stiefel-Whitney class
Orientation reversing isometries of H3
description Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. The properties of the 'square map' and other related maps serve as a technical step towards the counting of the connected components of the variety of representations of π(N) in Isom(H). We show that the variety of representations hom(π(N), Isom (H)) has 2 connected components, which are distinguished by the Stiefel-Whitney classes of the associated flat bundle.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/258269
https://dx.doi.org/urn:doi:10.1007/s10711-022-00682-x
url https://ddd.uab.cat/record/258269
https://dx.doi.org/urn:doi:10.1007/s10711-022-00682-x
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 BES-2016-079278
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
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