The topology of asymptotically locally flat gravitational instantons

Details The topology of asymptotically locally flat gravitational instantons The topology of asymptotically locally flat gravitational instantons

2006-02-06

arxiv.org/abs/hep-th/0602053v4

Phys.Lett.B641:461-465,2006

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, LaTeX, no figures; Some typos corrected, slightly differs from the published version

Scientific paper

10.1016/j.physletb.2006.08.080

In this letter we demonstrate that the intersection form of the Hausel--Hunsicker--Mazzeo compactification of a four dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kahler forms of the hyper-Kahler gravitational instanton metric is exact. This leads to the topological classification of these spaces. The proof exploits the relationship between L^2 cohomology and U(1) anti-instantons over gravitational instantons recognized by Hitchin. We then interprete these as reducible points in a singular SU(2) anti-instanton moduli space over the compactification leading to the identification of its intersection form. This observation on the intersection form might be a useful tool in the full geometric classification of various asymptotically locally flat gravitational instantons.

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