Positive scalar curvature and exotic structures on simply connected four manifolds

Aditya Kumar; Balarka Sen

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arXiv · 2501.01113

Positive scalar curvature and exotic structures on simply connected four manifolds

Aditya Kumar·Balarka Sen

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Abstract

We address Gromov's band width inequality and Rosenberg's $S^1$-stability conjecture for simply connected smooth four manifolds. Both results are known to be false in dimension 4 due to counterexamples based on Seiberg-Witten invariants. Nevertheless we show that both of these results hold upon considering simply connected smooth four manifolds up to homeomorphism. We also obtain a related result for non-simply connected smooth four manifolds.

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Aditya Kumar, Balarka Sen. 2025-01-02. Positive scalar curvature and exotic structures on simply connected four manifolds. https://arxiv.org/abs/2501.01113

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