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Compact manifolds of dimension with positive isotropic curvature
We prove the following result: Let be a compact manifold of
dimension with positive isotropic curvature. Then is
diffeomorphic to a spherical space form, or a compact quotient manifold of
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 . 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
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