On certain homological invariant and its relation with poincaré duality pairs
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Let G be a group, S = {Si, i ∈ I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a ℤ2 G-module. In [4] the authors defined a homological invariant E∗ (G, S, M), which is “dual” to the cohomological invariant E(G, S, M), defined in [1]. In this paper we present a more general treatment of the invariant E∗ (G, 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, 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.
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Algebra and Discrete Mathematics, v. 25, n. 2, p. 177-187, 2018.
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