Asymptotically flat manifolds with strong holonomy control are torus bundles over ALE ends, which yields Hitchin-Thorpe inequalities for Ricci-flat 4-manifolds and rigidity of Ricci-flat metrics on R^4.
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On the geometry of asymptotically flat manifolds
Asymptotically flat manifolds with strong holonomy control are torus bundles over ALE ends, which yields Hitchin-Thorpe inequalities for Ricci-flat 4-manifolds and rigidity of Ricci-flat metrics on R^4.