Manifolds with positive isotropic curvature of dimension at least nine

Zhengnan Chen

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arXiv · 2410.21078

Manifolds with positive isotropic curvature of dimension at least nine

Zhengnan Chen

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Abstract

In [Bre19], Simon Brendle showed that any compact manifold of dimension $n\geq12$ with positive isotropic curvature and contains no nontrivial incompressible $(n-1)-$dimensional space form is diffeomorphic to a connected sum of finitely many spaces, each of which is a quotient of $S^n$ or $S^{n-1}\times \mathbb{R}$ by standard isometries. We show that this result is actually true for $n\geq9$.

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Zhengnan Chen. 2024-10-28. Manifolds with positive isotropic curvature of dimension at least nine. https://arxiv.org/abs/2410.21078

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