The topology of asymptotically locally flat gravitational instantons

摘要

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 their topological classification.