We prove the following result: Let (M,g0β) be a compact manifold of
dimension nβ₯12 with positive isotropic curvature. Then M is
diffeomorphic to a spherical space form, or a compact quotient manifold of
Snβ1ΓR by diffeomorphisms, or a connected sum of
a finite number of such manifolds. This extends a recent work of Brendle, and
implies a conjecture of Schoen and a conjecture of Gromov in dimensions nβ₯12. The proof uses Ricci flow with surgery on compact orbifolds with isolated
singularities.Comment: 32 pages, proof of Theorem 1.1 and Corollary 1.2 clarifie