Adapted splittings for pairs (G,W)

Detalhes bibliográficos
Autor(a) principal: Andrade, Maria Gorete Carreira [UNESP]
Data de Publicação: 2019
Outros Autores: de Lourdes Campello Fanti, Ermínia [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.topol.2018.11.026
http://hdl.handle.net/11449/189949
Resumo: Let G be a group, W a G-set with [G:Gw]=∞ for all w∈W, where Gw denotes the point stabilizer of w∈W. Considering the restriction map resW G:H1(G,Z2G)→∏w∈EH1(Gw,Z2G), where E is a set of orbit representatives for the G-action in W, we define an algebraic invariant denoted by E‾(G,W). In this paper, by using the relation of this invariant with the end e(G) defined by Freudenthal–Hopf–Specker and a Swarup's Theorem about splittings of groups adapted to a family of subgroups, we show, for G finitely generated and W a G-set which falls into many finitely G-orbits, that (G,W) is adapted if, and only if, E‾(G,W)≥2.
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spelling Adapted splittings for pairs (G,W)Cohomology of groupsDualityEnds of groupsSplitting of groupsLet G be a group, W a G-set with [G:Gw]=∞ for all w∈W, where Gw denotes the point stabilizer of w∈W. Considering the restriction map resW G:H1(G,Z2G)→∏w∈EH1(Gw,Z2G), where E is a set of orbit representatives for the G-action in W, we define an algebraic invariant denoted by E‾(G,W). In this paper, by using the relation of this invariant with the end e(G) defined by Freudenthal–Hopf–Specker and a Swarup's Theorem about splittings of groups adapted to a family of subgroups, we show, for G finitely generated and W a G-set which falls into many finitely G-orbits, that (G,W) is adapted if, and only if, E‾(G,W)≥2.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)IBILCE - UNESP - São Paulo State University, Rua Cristovão Colombo, 2265IBILCE - UNESP - São Paulo State University, Rua Cristovão Colombo, 2265FAPESP: 2012/24454-8Universidade Estadual Paulista (Unesp)Andrade, Maria Gorete Carreira [UNESP]de Lourdes Campello Fanti, Ermínia [UNESP]2019-10-06T16:57:25Z2019-10-06T16:57:25Z2019-02-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article17-24http://dx.doi.org/10.1016/j.topol.2018.11.026Topology and its Applications, v. 253, p. 17-24.0166-8641http://hdl.handle.net/11449/18994910.1016/j.topol.2018.11.0262-s2.0-850580150133186337502957366Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengTopology and its Applicationsinfo:eu-repo/semantics/openAccess2021-10-22T21:16:11Zoai:repositorio.unesp.br:11449/189949Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:22:00.698756Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Adapted splittings for pairs (G,W)
title Adapted splittings for pairs (G,W)
spellingShingle Adapted splittings for pairs (G,W)
Andrade, Maria Gorete Carreira [UNESP]
Cohomology of groups
Duality
Ends of groups
Splitting of groups
title_short Adapted splittings for pairs (G,W)
title_full Adapted splittings for pairs (G,W)
title_fullStr Adapted splittings for pairs (G,W)
title_full_unstemmed Adapted splittings for pairs (G,W)
title_sort Adapted splittings for pairs (G,W)
author Andrade, Maria Gorete Carreira [UNESP]
author_facet Andrade, Maria Gorete Carreira [UNESP]
de Lourdes Campello Fanti, Ermínia [UNESP]
author_role author
author2 de Lourdes Campello Fanti, Ermínia [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Andrade, Maria Gorete Carreira [UNESP]
de Lourdes Campello Fanti, Ermínia [UNESP]
dc.subject.por.fl_str_mv Cohomology of groups
Duality
Ends of groups
Splitting of groups
topic Cohomology of groups
Duality
Ends of groups
Splitting of groups
description Let G be a group, W a G-set with [G:Gw]=∞ for all w∈W, where Gw denotes the point stabilizer of w∈W. Considering the restriction map resW G:H1(G,Z2G)→∏w∈EH1(Gw,Z2G), where E is a set of orbit representatives for the G-action in W, we define an algebraic invariant denoted by E‾(G,W). In this paper, by using the relation of this invariant with the end e(G) defined by Freudenthal–Hopf–Specker and a Swarup's Theorem about splittings of groups adapted to a family of subgroups, we show, for G finitely generated and W a G-set which falls into many finitely G-orbits, that (G,W) is adapted if, and only if, E‾(G,W)≥2.
publishDate 2019
dc.date.none.fl_str_mv 2019-10-06T16:57:25Z
2019-10-06T16:57:25Z
2019-02-15
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://dx.doi.org/10.1016/j.topol.2018.11.026
Topology and its Applications, v. 253, p. 17-24.
0166-8641
http://hdl.handle.net/11449/189949
10.1016/j.topol.2018.11.026
2-s2.0-85058015013
3186337502957366
url http://dx.doi.org/10.1016/j.topol.2018.11.026
http://hdl.handle.net/11449/189949
identifier_str_mv Topology and its Applications, v. 253, p. 17-24.
0166-8641
10.1016/j.topol.2018.11.026
2-s2.0-85058015013
3186337502957366
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Topology and its Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 17-24
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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