Polynomial modules over the Steenrod algebra and conjugation in the Milnor basis

Monks, Kenneth G.

doi:10.1090/S0002-9939-1994-1207540-3

Polynomial modules over the Steenrod algebra and conjugation in the Milnor basis
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by Kenneth G. Monks PDF

Proc. Amer. Math. Soc. 122 (1994), 625-634 Request permission

Abstract:

Let ${P_s} = {\mathbb {F}_2}[{x_1}, \ldots ,{x_s}]$ be the $\bmod \;2$ cohomology of the s-fold product of $\mathbb {R}{{\text {P}}^\infty }$ with the usual structure as a module over the Steenrod algebra. A monomial in ${P_s}$ is said to be hit if it is in the image of the action $\bar A \otimes {P_s} \to {P_s}$ where $\bar A$ is the augmentation ideal of A. We extend a result of Wood to determine a new family of hit monomials in ${P_s}$. We then use similar methods to obtain a generalization of antiautomorphism formulas of Davis and Gallant.

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