Free Abelian cohomology of groups and ends of universal covers (Q1065932)

Let G be a group possessing a K(G,1)-complex X with finite n-skeleton and \(\tilde X^ n\) the n-skeleton of the universal cover of X. The author explains the relationship between proper homotopy invariants at \(\infty\) of \(\tilde X^ n\) and \(H^*(G,ZG)\). In particular, if G is an appropriate extension of an infinite group, new results about \(H^*(G,ZG)\) and the proper homotopy type of \(\tilde X^ n\) are obtained. It can be used to get information about \(H^*(G,ZG)\) in situations where homological methods fail. A part of these results has been proved earlier by \textit{J. Dydak} [cf. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys. 27, 717-721 (1979; Zbl 0451.55005)].