On certain homological invariant and its relation with Poincaré duality pairs

Abstract

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 Z₂G-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.