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A Codimension Two Approach to the $\mathbb{S}^1$-Stability Conjecture
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abstract
J. Rosenberg's $\mathbb{S}^1$-stability conjecture states that a closed oriented manifold $X$ admits a positive scalar curvature metric iff $X\times \mathbb{S}^1$ admits a positive scalar curvature metric $h$. As pointed out by J. Rosenberg and others, there are known counterexamples in dimension four. We prove this conjecture whenever $h$ satisfies a geometric bound which measures the discrepancy between $\partial_\theta\in T\mathbb{S}^1$ and the normal vector field to $X\times \{P\}$, for a fixed $P\in \mathbb{S}^1.$
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Cited by 2 Pith papers
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