The topology of asymptotically locally flat gravitational instantons
Abstract
Description
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.
9 pages, LaTeX, no figures; Some typos corrected, slightly differs from the published version
9 pages, LaTeX, no figures; Some typos corrected, slightly differs from the published version