Global N∞$N_\infty$‐operads

Abstract

We define 𝑁 ∞ -operads in the globally equivariant setting and completely classify them. These global 𝑁 ∞operads model intermediate levels of equivariant commutativity in the global world, that is, in the setting where objects have compatible actions by all compact Lie groups. We classify global 𝑁 ∞ -operads by giving an equivalence between the homotopy category of global 𝑁 ∞ -operads and the partially ordered set of global transfer systems, which are much simpler, algebraic objects. We also explore the relation between global 𝑁 ∞ -operads and 𝑁 ∞ -operads for a single group, recently introduced by Blumberg and Hill. One interesting consequence of our results is the fact that not all equivariant 𝑁 ∞ -operads can appear as restrictions of global 𝑁 ∞ -operads.

Operads in unstable global homotopy theory

“…These operads in orthogonal spaces are the global analogs of N 1 -operads. A classification of them will appear in a separate article [1].…”