NDLI: Quotients of gravitational instantons

Content Provider	Springer Nature Link
Author	Wright, Evan P.
Copyright Year	2011
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.
Ending Page	108
Page Count	18
Starting Page	91
File Format	PDF
ISSN	0232704X
e-ISSN	15729060
Journal	Annals of Global Analysis and Geometry
Issue Number	1
Volume Number	41
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-05-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Eta-invariants, Chern-Simons invariants Theoretical, Mathematical and Computational Physics Eta invariant Fundamental groups and their automorphisms Gravitational instanton Geometry Hermitian and KÃ¤hlerian manifolds Asymptotically locally Euclidean Statistics for Business/Economics/Mathematical Finance/Insurance Analysis Group Theory and Generalizations Special Riemannian manifolds (Einstein, Sasakian, etc.) 4-Manifold
Content Type	Text
Resource Type	Article
Subject	Analysis Geometry and Topology

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