The cohomology theory of groups arose from both topological and algebraic sources. The starting point for the topological aspect of the theory was the work of Hurewicz  on “aspherical spaces.” About a year earlier, Hurewicz had introduced the higher homotopy groups π n X of a space X (n ≥ 2). He now singled out for study those path-connected spaces X whose higher homotopy groups are all trivial, but whose fundamental group π = π1X need not be trivial. Such spaces are called aspherical.
KeywordsSpectral Sequence Euler Characteristic Chapter VIII Homological Algebra Cohomology Theory
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