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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the action of Steenrod squares on polynomial algebras


Author: William M. Singer
Journal: Proc. Amer. Math. Soc. 111 (1991), 577-583
MSC: Primary 55S10; Secondary 55Q10, 55Q40, 55S05, 55T15
MathSciNet review: 1045150
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Abstract: Let $ {P_s}$ be the $ \bmod - 2$ cohomology of the elementary abelian group $ (Z/2Z) \times \cdots \times (Z/2Z)$ ($ s$ factors). The $ \bmod - 2$ Steenrod algebra $ A$ acts on $ {P_s}$ according to well-known rules. If $ {\mathbf{A}} \subset A$ denotes the augmentation ideal, then we are interested in determining the image of the action $ {\mathbf{A}} \otimes {P_s} \to {P_s}$: the space of elements in $ {P_s}$ that are hit by positive dimensional Steenrod squares. The problem is motivated by applications to cobordism theory [P1] and the homology of the Steenrod algebra [S]. Our main result, which generalizes work of Wood [W], identifies a new class of hit monomials.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045150-9
PII: S 0002-9939(1991)1045150-9
Article copyright: © Copyright 1991 American Mathematical Society