Additive cohomology operations

Duflot, Jeanne

doi:10.1090/S0002-9947-1989-0942425-1

Additive cohomology operations
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Trans. Amer. Math. Soc. 316 (1989), 311-325 Request permission

Abstract:

The bigraded group $\{ {H_i}({\Sigma _n},{\mathbf {Z}}/p)\}$ 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 $\bmod {\text { - }}p$ 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 $\bmod {\text { - }}p$ cohomology to write down two (additive) bases of the bigraded vector space of primitives of the above Hopf algebra.

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