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, the authors show that the connected sum M#W admits no complete metric of positive scalar curvature. When W = T ⁿ, this provides a positive answer to the generalized Geroch conjecture in the spin setting.

Keywords

Positive scalar curvature / Connected sum / Spin manifolds

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