N∞-operads and associahedra

We provide a combinatorial approach to studying the collection of $N_{\infty}$ -operads in $G$ -equivariant homotopy theory for $G$ a finite cyclic group of prime power order. In particular, we show that for $G = C_{p^{n}}$ the natural order on the collection of $N_{\infty}$ -operads is in bijection with the poset structure of the $(n + 1)$ -associahedron. We further provide a lower bound for the number of possible $N_{\infty}$ -operads for any finite cyclic group $G$ . As such, we have reduced an intricate problem in equivariant homotopy theory to a manageable combinatorial problem.

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Keywords

operads, equivariant spectra, ring spectra, associahedra, Catalan numbers

Mathematical Subject Classification 2010

Primary: 18D50, 55P91

Secondary: 06A07, 52B20, 55N91

Milestones

Received: 9 March 2020

Revised: 10 January 2021

Accepted: 8 July 2021

Published: 19 January 2022

Authors

Scott Balchin
Max Planck Institute for Mathematics Bonn Germany

David Barnes
Mathematical Sciences Research Centre Queen’s University Belfast United Kingdom

Constanze Roitzheim
School of Mathematics, Statistics and Actuarial Science University of Kent Canterbury United Kingdom

Vol. 315, No. 2, 2021

Scott Balchin, David Barnes and Constanze Roitzheim

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors