A model for configuration spaces of points

Abstract

We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected such manifold only depends on the real homotopy type of the manifold. Moreover, we show that for framed $D$-dimensional manifolds these models capture a natural right homotopy action of the little $D$-disks operad.