Exotic R⁴'s and positive isotropic curvature

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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 [Hu1], and was stated in [Hu2] 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.