On the generalized Geroch conjecture for complete spin manifolds
Abstract
Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold, we show that the connected sum M\# W admits no complete metric of positive scalar curvature. When W=Tn, this provides a positive answer to the generalized Geroch conjecture in the spin setting.
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