• Kenneth S. Brown
Part of the Graduate Texts in Mathematics book series (GTM, volume 87)


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 [1936] 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.


Spectral Sequence Euler Characteristic Chapter VIII Homological Algebra Cohomology Theory 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Kenneth S. Brown
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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