$N_\infty$-operads and associahedra

TL;DR

This paper introduces a combinatorial framework linking N-infinity-operads in G-equivariant homotopy theory for cyclic groups to associahedra, revealing a bijection with their poset structures and providing bounds on their quantity.

Contribution

It establishes a novel combinatorial approach connecting N-infinity-operads with associahedra and characterizes their structure for cyclic groups.

Findings

Bijection between N-infinity-operads and associahedra for cyclic groups

Lower bounds on the number of N-infinity-operads for finite cyclic groups

New combinatorial perspective on equivariant operads

Abstract

We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the collection of N-infinity-operads stands in bijection with the poset structure of the (n+1)-associahedron. We further provide a lower bound for the number of possible N-infinity-operads for any finite cyclic group G.