Adapted splittings for pairs (G,W)
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808128798920540160 |