Abstract
Recall that one obtains homology groups with coefficient group G by the following process:
-
(a)
Start with the chain complex C(X, A) = {Cq(X, A), ∂q}.
-
(b)
Apply the functor ⊗G to obtain the new chain complex.
C(X, A) ∂ G = C(X, A; G).
-
(c)
Take the homology groups of the resulting chain complex:
Hq(X, A; G) = Hq(C(X, A; G)).
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References
W. S. Massey, Homology and Cohomology Theory: An Approach Based on Alexander-Spanier Cochains, Marcel Dekker, Inc., New York, 1978, Chapter 8, §8.
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© 1991 Springer Science+Business Media, LLC
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Massey, W.S. (1991). Cohomology Theory. In: A Basic Course in Algebraic Topology. Graduate Texts in Mathematics, vol 127. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9063-4_12
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DOI: https://doi.org/10.1007/978-1-4939-9063-4_12
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