Cohomology作用素について

概要

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There are two methods of constructing the cohomology operations. The first which is given by N. E. Steenrod is defined by the n-th powers of complexes and the action of the cyclic group on the factors; i.e. the reduced power operations. The second makes use of the Eilenberg-MacLane complexes. Each method has its own advantage. But we could bring the two methods together in one. The basis for this is the theorem by A. Bold and R. Thorn. Their assertion, in a word, is that there are isomorphisms πi(SP∞(X))≈H_i(X),(X),i≧1, where SP∞(X) is the infinite symmetric product of a space X. This offers an entirely new method of constructing Elenberg-MacLane complexes. And we can define a homomorphism H^r(W[○!×πM^n)→H^r(SP^n(M)), where H^r(W[○!×πM^n) is the cohomology group that determins the reduced power operations. These facts give us a clue for solving the problem.
東京女子大学の論文
1958-12-20