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arXiv · 2503.13815

On the topology of manifolds with positive intermediate curvature

Liam Mazurowski·Tongrui Wang·Xuan Yao
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Abstract

We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive $m$-intermediate curvature. We prove the result for manifolds of dimension $n\in\{3,4,5\}$ and for most choices of $m$ when $n=6$. As a corollary, we show that a closed, aspherical 6-manifold cannot admit a metric with positive $4$-intermediate curvature.

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Liam Mazurowski, Tongrui Wang, Xuan Yao. 2025-03-18. On the topology of manifolds with positive intermediate curvature. https://arxiv.org/abs/2503.13815

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