  In this paper, we investigate the geometry of asymptotically flat manifolds
with controlled holonomy. We show that any end of such manifold admits a torus
fibration over an ALE end. In addition, we prove a Hitchin-Thorpe inequality
for oriented Ricci-flat $4$-manifolds with curvature decay and controlled
holonomy. As an application, we show that any complete asymptotically flat
Ricci-flat metric on a $4$-manifold which is homeomorphic to $\mathbb R^4$ must
be isometric to the Euclidean or the Taub-NUT metric, provided that the tangent
cone at infinity is not $\mathbb R \times \mathbb R_+$.
