Cohomology Theory

  • William S. Massey
Part of the Graduate Texts in Mathematics book series (GTM, volume 70)


Recall that one obtains homology groups with coefficient group G by the following process:
  1. (a)

    Start with the chain complex C(X,A) = {Cq(X,A),∂q}.

  2. (b)
    Apply the functor ⊗G to obtain the new chain comples
    $$ C\left( {X,A} \right) \otimes G = C\left( {X,A;G} \right).$$
  3. (c)
    Take the homology groups of the resulting chain complex:
    $$ H_q \left( {X,A;G} \right) = H_q \left( {C\left( {X,A;G} \right)} \right).$$


Manifold Lime 


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Bibliography for Chapter VII

  1. [1]
    W. S. Massey, Homology and Cohomology Theory : An Approach Based on Alexander—Spanier Cochains, Marcel Dekker, Inc., New York, 1978, Chapter 8, §8.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • William S. Massey
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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