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Annals of Global Analysis and Geometry

, Volume 41, Issue 1, pp 91–108 | Cite as

Quotients of gravitational instantons

  • Evan P. WrightEmail author
Original Paper

Abstract

A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a Gibbons–Hawking space. The possible quotients are described in terms of the monopole set in \({\mathbb{R}^3}\) , and it is proved that every such quotient is actually Kähler. The fact that the Gibbons–Hawking spaces are the only gravitational instantons to admit isometric quotients is proved by examining the possible fundamental groups at infinity: most can be ruled out by the classification of three-dimensional spherical space form groups, and the rest are excluded by a computation of the Rohklin invariant (in one case) or the eta invariant (in the remaining family of cases) of the corresponding space forms.

Keywords

Gravitational instanton Asymptotically locally Euclidean Eta invariant 4-Manifold 

Mathematics Subject Classification (2000)

Primary: 53C25 Secondary: 53C55 58J28 20F34 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentStony Brook UniversityStony BrookUSA

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