Geometry and topology · Oct 6, 2026
Nonnegative-curvature Einstein classification and an L2 topological gap
Classifies closed connected Einstein four-manifolds with positive Einstein constant and nonnegative sectional curvature: up to scaling, their universal Riemannian covers are the round S4, Fubini–Study , or a product of equal round two-spheres. A closed simply connected nonnegatively curved four-manifold is diffeomorphic to one of these whenever the scale-invariant L2 norm of its trace-free Ricci curvature lies below a universal positive constant.
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