On the topology of manifolds with positive intermediate curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917959432142848 |
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| author | Mazurowski, Liam Wang, Tongrui Yao, Xuan |
| author_facet | Mazurowski, Liam Wang, Tongrui Yao, Xuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the topology of manifolds with positive intermediate curvature Mazurowski, Liam Wang, Tongrui Yao, Xuan Differential Geometry Geometric Topology 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. |
| title | On the topology of manifolds with positive intermediate curvature |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2503.13815 |