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arXiv · 2204.09184

On the generalized Geroch conjecture for complete spin manifolds

Xiangsheng Wang·Weiping Zhang
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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 $W=T^n$, this provides a positive answer to the generalized Geroch conjecture in the spin setting.

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Xiangsheng Wang, Weiping Zhang. 2022-04-20. On the generalized Geroch conjecture for complete spin manifolds. https://doi.org/10.1007/s11401-022-0381-y

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