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Title:
On the moduli space of critical metrics on connected sums of Einstein four-manifolds
Speaker:
Abstract:
In joint work with Gursky, critical metrics for quadratic Riemannian functionals on certain connected sums was previously obtained using a gluing procedure. After discussing some background of this gluing problem, I will present some recent results regarding the computation of the quadratic term in the expansion of the Kuranishi map for this construction in the case of the blow-up of CP^2 at a point. The computation is quite non-trivial, since (i) this term is fundamentally a global geometric invariant and is not determined alone by local geometric invariants, and (ii) this term depends crucially on the explicit nonlinear structure of the critical equation. There is an interesting connection between these critical metrics and a family of Kahler constant scalar curvature metrics with edge-cone singularities along two divisors.
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