Diagrams encoding group actions on $\Gamma$-spaces

Abstract

We introduce, for any group $G$, a category $G\Gamma$ such that diagrams $G\Gamma \to \mathcal{SS}ets$ satisfying a Segal condition correspond to infinite loop spaces with a $G$-action. We also consider diagrams which encode group actions on infinite loop spaces where the group may vary.

To appear in Proceedings of the Conference on Manifolds, K-Theory, and Related Topics, Contemporary Mathematics (AMS)