Scattering Configuration Spaces

For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xn sc which is a compact manifold with corners for each n; coinciding with the previously known cases for n = 2; 3: It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn: The resulting space is shown to map smoothly, by a bbration, covering the usual projection, to the lower stretched products. It is anticipated that this manifold with corners, or at least its combinatorial structure, is a universal model for phenomena on asymptotically at manifolds in which particle clusters emerge at in nity. In particular this is the case for magnetic monopoles on R in which case these spaces are closely related to compacti cations of the moduli spaces with the boundary faces mapping to lower charge idealized moduli spaces.