We prove the following result: Let $(M,g_0)$ be a complete noncompact manifold of dimension $n\geq 12$ with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded below. Then there is a finite collection $\mathcal{ X}$ of spherical $n$-manifolds and manifolds of the form $\mathbb{ S}^{ n-1} \times \mathbb{ R} /G$, where $G$ is a discrete subgroup of the isometry group of the round cylinder $\mathbb{ S}^{ n-1}\times \mathbb{ R}$, such that $M$ is diffeomorphic to a (possible infinite) connected sum of members of $\mathcal{ X}$. This extends a recent work of Huang. The proof uses Ricci flow with surgery on open orbifolds with isolated singularities.
Categories: math.DG math.AP math.GT