Realizing Transfer Systems as Suboperads of Coinduced Operads

Abstract

In this paper, we present an explicit method to identify equivariant suboperads of coinduced operads that contain only fixed points associated to any desired transfer system. Our method works for a class of operads that we call intersection operads, which includes many familiar operads of interest, including the little $k$-cube operads, the Steiner operad, and the linear isometries operad. As an application, we also construct an intersection $\mathbb{E}_\infty$-operad that, when applying our construction, will produce a $\mathbb{N}_\infty$-operad realizing an arbitrary transfer system.