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arXiv · 1705.00553

Positive scalar curvature and connected sums

Guangxiang Su·Weiping Zhang
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Abstract

Let $N$ be a closed enlargeable manifold in the sense of Gromov-Lawson and $M$ a closed spin manifold of equal dimension, a famous theorem of Gromov-Lawson states that the connected sum $M\# N$ admits no metric of positive scalar curvature. We present a potential generalization of this result to the case where $M$ is nonspin. We use index theory for Dirac operators to prove our result.

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Guangxiang Su, Weiping Zhang. 2017-05-24. Positive scalar curvature and connected sums. https://arxiv.org/abs/1705.00553

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