Geodesic
On certain homological invariant and its relation with Poincar\'{e} duality pairs
Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 177-187

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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
Mots-clés : homological invariant. 
@article{ADM_2018_25_2_a1,
     author = {Maria Gorete Carreira Andrade and Amanda Buosi Gazon and Amanda Ferreira de Lima},
     title = {On certain homological invariant and its relation with {Poincar\'{e}} duality pairs},
     journal = {Algebra and discrete mathematics},
     pages = {177--187},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a1/}
}
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Maria Gorete Carreira Andrade; Amanda Buosi Gazon; Amanda Ferreira de Lima. On certain homological invariant and its relation with Poincar\'{e} duality pairs. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 177-187. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a1/