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Cohomology with Chains as Coefficients
Author(s) -
Brown R.
Publication year - 1964
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-14.3.545
Subject(s) - citation , cohomology , mathematics , computer science , library science , pure mathematics
THE cohomology theory described in the title is obtained by replacing the usual coefficient group by an arbitrary chain complex. This theory satisfies all of the Eilenberg-Steenrod axioms for a cohomology theory except the dimension axiom. There are other theories with this property, and among these our theory is probably the least extraordinary. That is to say, its definition and techniques are very similar to those of the usual cohomology theory. The theory is justified by its applications. The first of these is a very simple construction f of the Kiinneth isomorphism