Free circle actions and positive Ricci curvature on manifolds with the cohomology ring of $S^2\times S^5$

Philipp Reiser

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arXiv · 2603.29838

Free circle actions and positive Ricci curvature on manifolds with the cohomology ring of $S^2\times S^5$

Philipp Reiser

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Abstract

We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of $S^2\times S^5$ admit a free circle action. In addition, we show that whenever such an action exists, there exist infinitely many pairwise non-equivalent free circle actions. Finally, in almost all cases where such an action exists, we construct invariant Riemannian metrics of positive Ricci curvature.

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Philipp Reiser. 2026-03-31. Free circle actions and positive Ricci curvature on manifolds with the cohomology ring of $S^2\times S^5$. https://arxiv.org/abs/2603.29838

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