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On Optimal 4-Dimensional Metrics

Authors:	Claude LeBrun Bernard Maskit

Institution:	(1) Mathematics Department, SUNY, Stony Brook, NY 11794-3651, USA

Abstract:	We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum $\overline{ {\mathbb{C}\mathbb{P}}}_{2}\#\overline{ {\mathbb{C}\mathbb{P}}}_{2}\#\overline{ {\mathbb{C}\mathbb{P}}}_{2}\#\overline{ {\mathbb{C}\mathbb{P}}}_{2}\#\overline{ {\mathbb{C}\mathbb{P}}}_{2}$ of five reverse-oriented complex projective planes admits such metrics. Supported in part by NSF grant DMS-0604735.

Keywords:	4-manifold Anti-self-dual metric Scalar curvature Kleinian group
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