Exotic [formula omitted]'s and positive isotropic curvature

Abstract

We show that no exotic R4 admits a complete Riemannian metric with uniformly positive isotropic curvature and with bounded geometry. This is essentially a corollary of the main result in [7], and was stated in [8] without proof. In the process of the proof we also show that the diffeomorphism type of an infinite connected sum of some connected smooth n-manifolds (n≥2) according to a locally finite graph does not depend on the gluing maps used.