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Let be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for . We show that on any spin surgery of along a region whose induced homomorphism on the fundamental group is trivial, every complete metric with non-negative scalar curvature is Ricci-flat. In particular, on the connected sum of with a spin manifold, any complete metric with non-negative scalar curvature is Ricci-flat.

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