ar X iv : 0 80 8 . 20 22 v 1 [ m at h . D G ] 1 4 A ug 2 00 8 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 b-fibration, 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 flat manifolds in which particle clusters emerge at infinity. In particular this is the case for magnetic monopoles on R in which case these spaces are closely related to compactifications of the moduli spaces with the boundary faces mapping to lower charge idealized moduli spaces.