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Lifting $N_\infty$ operads from conjugacy data

Scott Balchin, Ethan MacBrough and Kyle Ormsby

Vol. 5 (2023), No. 3, 479–504
Abstract

We isolate a class of groups — called lossless groups — for which homotopy classes of G-N operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes Sub (G)G.

Keywords
homotopical combinatorics, equivariant homotopy, N-infinity operads, subgroup lattice, subgroup fusion
Mathematical Subject Classification
Primary: 06B05, 20D30, 20J99, 55P91
Milestones
Received: 12 October 2022
Revised: 25 February 2023
Accepted: 11 March 2023
Published: 2 November 2023
Authors
Scott Balchin
Mathematical Sciences Research Centre
Queen’s University Belfast
Belfast
UK
Ethan MacBrough
Department of Mathematics and Statistics
Reed College
Portland, OR
United States
Kyle Ormsby
Department of Mathematics and Statistics
Reed College
Portland, OR
United States
Department of Mathematics
University of Washington
Seattle, WA
United States