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Curvature, cones and characteristic numbers

Published online by Cambridge University Press:  25 April 2013

MICHAEL ATIYAH  and
CLAUDE LEBRUN
MICHAEL ATIYAH
Affiliation:
School of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ. e-mail: [email protected]
CLAUDE LEBRUN
Affiliation:
Department of Mathematics, SUNY, Stony Brook, NY 11794-3651, U.S.A. e-mail: [email protected]
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Abstract

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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 of such edge-cone manifolds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 13 - 37
Copyright
Copyright © Cambridge Philosophical Society 2013 

References

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