#### Volume 21, issue 1 (2021)

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

### Inbar Klang, Alexander Kupers and Jeremy Miller

Algebraic & Geometric Topology 21 (2021) 105–136
##### Abstract

We describe an ${\mathsc{ℰ}}_{k}$–cell structure on the free ${\mathsc{ℰ}}_{k+1}$–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 ${\mathsc{ℰ}}_{k+m}$–algebra on a point by iterated pushouts of free ${\mathsc{ℰ}}_{k}$–algebras.

##### Keywords
little disks operad, cell attachments, delooping, May–Milgram filtration, iterated loop spaces, configuration spaces
##### Mathematical Subject Classification 2010
Primary: 55P48
Secondary: 18D50, 55R40, 55R80