Free Abelian cohomology of groups and ends of universal covers. (English) Zbl 0577.20024

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 J. Dydak [cf. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys. 27, 717-721 (1979; Zbl 0451.55005)].
Reviewer: M.Golasiński


20F65 Geometric group theory
20J05 Homological methods in group theory
57M10 Covering spaces and low-dimensional topology
57Q05 General topology of complexes
55P20 Eilenberg-Mac Lane spaces


Zbl 0451.55005
Full Text: DOI


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