Mathematics – Differential Geometry
Scientific paper
2011-02-11
Mathematics
Differential Geometry
22 pages. Typographical errors corrected
Scientific paper
A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperk\"ahler (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 R^3, and it is proved that every such quotient is actually K\"ahler. 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 3-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.
No associations
LandOfFree
Quotients of gravitational instantons does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quotients of gravitational instantons, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quotients of gravitational instantons will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-84461