Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

A class of left ideals of the Steenrod algebra

Pages: 185 – 191

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n1.a7

Authors

I. Johnson (Department of Mathematics, Willamette University, Salem, Oregon, U.S.A.)

J. L. Merzel (Department of Mathematics, Soka University of America, Aliso Viejo, California, U.S.A.)

Abstract

We study the nested collection of left ideals of $\mathcal{A}$, the mod 2 Steenrod algebra, $L(k) := \mathcal{A} \{\mathit{Sq}^{2^0}, \mathit{Sq}^{2^1}, \mathit{Sq}^{2^2}, \dots, \mathit{Sq}^{2^k}\}$. We determine the smallest $k$ such that $\mathit{Sq}^n \in L(k)$. We discuss an application which improves upon the results of F. R. Cohen and the first author in their paper comparing the loop of the degree 2 map on a sphere and the H-space squaring map on the loop of a sphere.

Keywords

Steenrod algebra; homotopy

2010 Mathematics Subject Classification

55S10

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