  We show the following result: Let $(M,g_0)$ be a compact manifold of
dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is
diffeomorphic to a spherical space form, or a quotient manifold of
$\mathbb{S}^{n-1}\times \mathbb{R}$ by a cocompact discrete subgroup of the
isometry group of the round cylinder $\mathbb{S}^{n-1}\times \mathbb{R}$, 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 the ambient
isotopy uniqueness of closed tubular neighborhoods of compact suborbifolds.

Differential Geometry