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:
    $$ H_q \left( {X,A;G} \right) = H_q \left( {C\left( {X,A;G} \right)} \right).$$


Abelian Group Exact Sequence Chain Complex Cohomology Group Short Exact Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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