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.