On certain homological invariant and its relation with Poincare duality pairs

Abstract

Let G be a group, S = {S-i, i is an element of I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a Z(2)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 Poincare duality for groups and pairs.