2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216403In 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 versionHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext