We consider topological moduli spaces of \(d\)-dimensional manifolds with \(k\) particles. In these moduli spaces the location of the particles is constrained by the \(d\)-dimensional manifold. We will compare this moduli space with the moduli space of \(d\)-dimensional manifolds in which the location of the particles is no longer constrained, ie is decoupled. Using recent homology stability results of Galatius–Randal-Williams and others we will generalise work by Boedigheimer–Tillmann from surfaces to higher dimensional manifolds. This is work in progress.