The May–Milgram filtration and $\mathcal{E}_k$–cells

Abstract

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