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Einstein Metrics, Four-Manifolds, and Differential Topology

Claude LeBrun
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Abstract

This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.

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Claude LeBrun. 2004-04-20. Einstein Metrics, Four-Manifolds, and Differential Topology. https://arxiv.org/abs/math/0404359

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