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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 k–cell structure on the free k+1–algebra on a point, and more generally describe how the May–Milgram filtration of ΩmΣmSk lifts to a filtration of the free k+m–algebra on a point by iterated pushouts of free k–algebras.

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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
References
Publication
Received: 9 September 2018
Revised: 23 November 2019
Accepted: 6 May 2020
Published: 25 February 2021
Authors
Inbar Klang
Department of Mathematics
Columbia University
New York, NY
United States
Alexander Kupers
Department of Computer and Mathematical Sciences
University of Toronto Scarborough
Toronto, ON
Canada
Jeremy Miller
Department of Mathematics
Purdue University
West Lafayette, IN
United States