Einstein Metrics, Four-Manifolds, and Differential Topology

Details Einstein Metrics, Four-Manifolds, and Differential Topology Einstein Metrics, Four-Manifolds, and Differential Topology

2004-04-20

arxiv.org/abs/math/0404359v1

Surveys in Differential Geometry, vol. VIII: Papers in Honor of Calabi, Lawson, Siu, and Uhlenbeck. S.-T. Yau, editor. Interna

Mathematics

Differential Geometry

21 pages, LaTeX2e

Scientific paper

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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