Lorenzo Foscolo (Stony Brook). MODULI SPACES OF MONOPOLES AND GRAVITATIONAL INSTANTONS

It is well-known that moduli spaces of anti-self-dual (ASD) connections on hyperkähler 4–manifolds are themselves hyperkähler. Using argument from physics, Cherkis and Kapustin suggested that “moduli spaces of solutions to dimensional reductions of the ASD equations are a natural place to look for gravitational instantons”, i.e. complete hyperkähler 4-manifolds with decaying curvature at infinity. The talk will focus on moduli spaces of monopoles with singularities on and . Thanks to work of Cherkis–Kapustin and others, when 4–dimensional these (are expected to) yield examples of gravitational instantons of type ALF and ALG, respectively. I will discuss a gluing construction in these two settings and show how it can be exploited to understand the asymptotic geometry of the moduli spaces.

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