Einstein Metrics, Four-Manifolds, and Differential Topology

2004/04/20 by Claude LeBrun
Mathematics · #math.DG #math.GT #msc:53C25 #msc:57R57

paper · pdf

published as Surveys in Differential Geometry, vol. VIII: Papers in Honor of Calabi, Lawson, Siu, and Uhlenbeck. S.-T. Yau, editor. International Press of Boston, 2003, pp. 235--255 · 21 pages, LaTeX2e

arxiv created 2004/04/20 · arxiv updated 2009/12/01

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.

Related

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• A survey of Einstein metrics on 4-manifolds