Curvature , Cones , and Characteristic Numbers

@inproceedings{Atiyah2012CurvatureC,
  title={Curvature , Cones , and Characteristic Numbers},
  author={Michael Atiyah and Claude Lebrun},
  year={2012}
}
We study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss–Bonnet and signature theorems for arbitrary Riemannian 4-manifolds with edge-cone singularities, and then show that these yield non-trivial obstructions in the Einstein case. We then use these integral formulæ to obtain interesting information regarding gravitational instantons which arise as limits… CONTINUE READING

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