Scattering configuration spaces


For a compact manifold with boundary XX we introduce the nn-fold scattering stretched product XscnX^n_{\text{sc}} which is a compact manifold with corners for each n,n, coinciding with the previously known cases for n=2,3.n=2,3. It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn.X^n. 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\mathbb{R}^3 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

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oaioai:eprints.ucl.ac.uk.OAI2:1390320Last time updated on 9/10/2013

This paper was published in UCL Discovery.

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