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A criterion for a monomial in P(3) to be hit

Published online by Cambridge University Press:  01 November 2008

A. S. JANFADA
A. S. JANFADA*
Affiliation:
Department of Mathematics, Urmia University, P.O. Box 165, Urmia, Iran. e-mail: [email protected]
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Abstract

Let P(n) = [x1, . . ., xn] = ⊕d≥0Pd(n) be the polynomial algebra viewed as a graded left module over the Steenrod algebra at the prime 2. The grading is by the degree of the homogeneous polynomials Pd(n) of degree d in the n variables x1, . . ., xn. The algebra P(n) realizes the cohomology of the product of n copies of infinite real projective space. We recall that a homogeneous element f of grading d in a graded left -module M is hit if there is a finite sum f = ΣiSqi(hi), called a hit equation, where the pre-images hi ∈ M have grading strictly less than d and the Sqi, called the Steenrod squares, generate . One of the important parts of the hit problem is to check whether a given polynomial in M is hit or not. In this article we study this problem in the 3-variable case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 587 - 599
Copyright
Copyright © Cambridge Philosophical Society 2008

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