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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 25, Issue 2, Pages 177–187 (Mi adm653)

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

Abstract: 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.

Keywords: (co)homology of groups, duality groups, duality pairs, homological invariant.

 Funding Agency Grant Number Fundação de Amparo à Pesquisa do Estado de São Paulo 2012/24454-8 Coordenaҫão de Aperfeiҫoamento de Pessoal de Nível Superior The first author was partially supported by FAPESP, grant no. 2012/24454-8 and the second and third authors were supported by CAPES.

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MSC: 20J05, 20J06, 57P10
Revised: 23.06.2017
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Citation: 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

Citation in format AMSBIB
\Bibitem{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}