The topology of asymptotically locally flat gravitational instantons
Abstract
In this Letter we demonstrate that the intersection form of the HauselHunsickerMazzeo compactification of a fourdimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kähler forms of the hyperKähler gravitational instanton metric is exact. This leads to their topological classification.
The proof exploits the relationship between L^{2} cohomology and U (1) antiinstantons over gravitational instantons recognized by Hitchin. We then interprete these as reducible points in a singular SU (2) antiinstanton 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.
 Publication:

Physics Letters B
 Pub Date:
 October 2006
 DOI:
 10.1016/j.physletb.2006.08.080
 arXiv:
 arXiv:hepth/0602053
 Bibcode:
 2006PhLB..641..461E
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 9 pages, LaTeX, no figures