The May-Milgram filtration and $E_k$-cells

Abstract

We describe an $E_k$-cell structure on the free $E_{k+1}$-algebra on a point, and more generally describe how the May-Milgram filtration of ${\Omega }^m{\Sigma }^m{S}^k$ lifts to a filtration of the free $E_{k+m}$-algebra on a point by iterated pushouts of free $E_k$-algebras.

25 pages, 3 figures. Final version, to appear in AG&T