Steenrod squares of polynomials and the Peterson conjecture. (English) Zbl 0692.55011

The author proves the following conjecture of F. Peterson: if \(H^*(RP^{\infty}\times...\times RP^{\infty};F_ 2)=F_ 2[X_ 1,...,X_ n]\) has an \({\mathfrak A}\)-module generator in degree d then \(\alpha (d+n)\leq n\). Here \(\alpha(K)\) is the number of ones in the dyadic expansion of k. The proof is based on the observation that if u, v are elements of an \({\mathfrak A}\)-algebra and \(\theta\in {\mathfrak A}\) then \(\chi(\theta)(u)\cdot v=u\cdot \theta(v)\) modulo image \(\tilde{\mathfrak A}\).
Reviewer: S.O.Kochman


55S10 Steenrod algebra
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[1] Steenrod, Cohomology Operations (1962)
[2] Peterson, Abstracts Amer. Math. Soc (1987)
[3] Peterson, Math. Proc. Cambridge Philos. Soc 105 pp 311– (1989)
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