Homology, Homotopy and Applications

A class of left ideals of the Steenrod algebra

Abstract

We study the nested collection of left ideals of $\mathcal{A}$, the mod 2 Steenrod algebra, $L(k) : = \mathcal{A}\{Sq^{2^0}, Sq^{2^1}, Sq^{2^2}, ... , Sq^{2^k}$. We determine the smallest k such that $Sq^n \in l (k)$. 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.

Article information

Source
Homology Homotopy Appl., Volume 9, Number 1 (2007), 185-191.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.hha/1175791092

Mathematical Reviews number (MathSciNet)
MR2280291

Zentralblatt MATH identifier
1111.55012

Subjects
Primary: 55S10: Steenrod algebra

Keywords
Steenrod algebra homotopy

Citation

Johnson, I.; Merzel, J. L. A class of left ideals of the Steenrod algebra. Homology Homotopy Appl. 9 (2007), no. 1, 185--191. https://projecteuclid.org/euclid.hha/1175791092