Scattering configuration spaces
- Publication date
- Publisher
Abstract
For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xscn​ 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 R3 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