On certain homological invariant and its relation with Poincaré duality pairs
Maria Gorete Carreira Andrade, Amanda Buosi Gazon, Amanda Ferreira Lima
Abstract
Let be a group, a non empty family of (not necessarily distinct) subgroups of infinite index in and a -module. In [4] the authors defined a homological invariant which is “dual” to the cohomological invariant defined in [1]. In this paper we present a more general treatment of the invariant obtaining results and properties, under a homological point of view, which are dual to those obtained by Andrade and Fanti with the invariant . We analyze, through the invariant , properties about groups that satisfy certain finiteness conditions such as Poincar\'e duality for groups and pairs.
Keywords
(co)homology of groups, duality groups, duality pairs, homological invariant
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