Operads in unstable global homotopy theory

Abstract

In this paper we study operads in unstable global homotopy theory, which is the homotopy theory of spaces with compatible actions by all compact Lie groups. We show that the theory of these operads works remarkably well, as for example it is possible to give a model structure for the category of algebras over any such operad. We define global $E_\infty$-operads, a good generalization of $E_\infty$-operads to the global setting, and we give a rectification result for algebras over them.