Additive cohomology operations

Author:
Jeanne Duflot

Journal:
Trans. Amer. Math. Soc. **316** (1989), 311-325

MSC:
Primary 55S05

DOI:
https://doi.org/10.1090/S0002-9947-1989-0942425-1

MathSciNet review:
942425

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Abstract: The bigraded group becomes a Hopf algebra, if multiplication is induced by restriction, and comultiplication is induced by transfer. Using Steenrod's method of considering elements of this bigraded group as cohomology operations, the primitives of this Hopf algebra correspond to additive cohomology operations. In this paper we use the results known about the homology and cohomology of the symmetric groups and the operations they induce in cohomology to write down two (additive) bases of the bigraded vector space of primitives of the above Hopf algebra.

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0942425-1

Article copyright:
© Copyright 1989
American Mathematical Society