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Band Width Inequality and S1-Stability up to Homeomorphism for Four-Manifolds

The result that Gromov's positive-scalar-curvature band-width inequality and Rosenberg's S1-stability conjecture, both false for smooth four-manifolds because of Seiberg-Witten counterexamples, hold for simply connected smooth four-manifolds when considered up to homeomorphism, proved with separating mu-bubble (minimal-hypersurface) methods.

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POSITIVE SCALAR CURVATURE AND EXOTIC STRUCTURES ON SIMPLY CONNECTED FOUR MANIFOLDS ADITYA KUMAR AND

Gromov's band-width inequality bounds how wide a Riemannian band can be while carrying positive scalar curvature, and Rosenberg's S1-stability conjecture predicts that a closed manifold admits a posi…