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Michael Singer : A new approach to monopole metrics

The moduli space of non-abelian magnetic euclidean monopoles is known to be a smooth manifold of dimension $4k$, and carries a natural complete riemannian metric. Here $k$, a positive integer, is a topological invariant of the monopole, its magnetic charge. The metric is hyperKaehler, and in particular Ricci-flat, and this is one of the reasons why these moduli spaces are popular with geometers and physicists. In this talk, I shall explain a new approach to the analysis of monopole metrics and some new results about their asymptotic behaviour. This will be a report on joint work with Richard Melrose and Chris Kottke.

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