Relative cohomology theory for profinite groups

Virtual pro-p properties of 3-manifold groups

“…The theory of the (co)homology of a profinite group relative to a collection of subgroups was defined and studied in [Wil17a]. We will state a restricted version of the definition here and leave it to the curious reader to read further.…”

“…We will state a restricted version of the definition here and leave it to the curious reader to read further. Definition 1.3 (Definition 2.1 of [Wil17a]). Let G be a pro-p group and S " tS 0 , .…”

“…for any G 1 -modules M and A as above, regarded as G-modules via φ. See Proposition 2.6 of [Wil17a].…”

“…Definition 1.4 (Theorem 5.15 of [Wil17a]). Let G be a pro-p group and S a collection of closed subgroups of G. Then pG, Sq is a PD n pair if…”

“…In this paper we will carry out this program in the realm of pro-p groups. The notions of 'relative (co)homology' and 'Poincaré duality pair' for profinite groups were defined and developed in the author's paper [Wil17a]. In the first part of this paper we will classify those pro-p group pairs which are Poincaré duality pairs of dimension 2.…”