Classification of compact manifolds with positive isotropic curvature

arXiv2305.18154MaRDI QIDQ6510327

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Abstract: We show the following result: Let $(M,g_0)$ be a compact manifold of dimension $ngeq12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a quotient manifold of $mathbb{S}^{n-1}imesmathbbR$ by a cocompact discrete subgroup of the isometry group of the round cylinder $mathbb{S}^{n-1}imesmathbbR$, or a connected sum of a finite number of such manifolds. This extends previous works of Brendle and Chen-Tang-Zhu, and improves a work of Huang. The proof uses Ricci flow with surgery on compact orbifolds, with the help of ambient isotopy uniqueness of closed tubular neighborhoods of compact suborbifolds.

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