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RESEARCH ARTICLE
On certain homological invariant and its relation with Poincaré duality pairs
Maria Gorete Carreira Andradea, Amanda Buosi Gazonb, Amanda Ferreira de Limab a Universidade Estadual Paulista, Departamento de Matemática, Rua Cristovão Colombo, 2265, 15054-000, São José do Rio Preto - SP, Brazil
b Universidade Federal de São Carlos, Departamento de Estatística, Rodovia Washington Luíis, km 235, 13565-905, São Carlos - SP, Brazil
Аннотация:
Let $G$ be a group, $\mathcal{S} = \{ S_i, i \in I\}$ a non empty family of (not necessarily distinct) subgroups of infinite index in $G$ and $M$ a $\mathbb{Z}_2 G$-module. In [4] the authors defined a homological invariant $E_*(G, \mathcal{S}, M),$ which is “dual” to the cohomological invariant $E(G, \mathcal{S}, M)$, defined in [1]. In this paper we present a more general treatment of the invariant $E_*(G, \mathcal{S}, M)$ obtaining results and properties, under a homological point of view, which are dual to those obtained by Andrade and Fanti with the invariant $E(G, \mathcal{S}, M)$. We analyze, through the invariant $E_{*}(G, S,M)$, properties about groups that satisfy certain finiteness conditions such as Poincaré duality for groups and pairs.
Ключевые слова:
(co)homology of groups, duality groups, duality pairs, homological invariant.
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Тип публикации:
Статья
MSC: 20J05, 20J06, 57P10 Поступила в редакцию: 19.08.2016 Исправленный вариант: 23.06.2017
Язык публикации: английский
Образец цитирования:
Maria Gorete Carreira Andrade, Amanda Buosi Gazon, Amanda Ferreira de Lima, “On certain homological invariant and its relation with Poincaré duality pairs”, Algebra Discrete Math., 25:2 (2018), 177–187
Цитирование в формате AMSBIB
\RBibitem{AndGazDe 18}
\by Maria Gorete Carreira~Andrade, Amanda~Buosi~Gazon, Amanda~Ferreira~de~Lima
\paper On certain homological invariant and its relation with Poincar\'{e} duality pairs
\jour Algebra Discrete Math.
\yr 2018
\vol 25
\issue 2
\pages 177--187
\mathnet{http://mi.mathnet.ru/adm653}
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http://mi.mathnet.ru/adm653 http://mi.mathnet.ru/rus/adm/v25/i2/p177
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