Positive scalar curvature and connected sums

Guangxiang Su; Weiping Zhang

Positive scalar curvature and connected sums

Differential Geometry 2017-05-25 v2

Authors: Guangxiang Su , Weiping Zhang

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.

Keywords

positive scalar curvature connected sum enlargeable manifold spin manifold Gromov-Lawson theorem Dirac operator index theory non-spin generalization

Cite

@article{arxiv.1705.00553,
  title  = {Positive scalar curvature and connected sums},
  author = {Guangxiang Su and Weiping Zhang},
  journal= {arXiv preprint arXiv:1705.00553},
  year   = {2017}
}

Comments

5 pages. Correct a mistake in the previous version. The result of the current version does not imply the original statement in the earlier version

Positive scalar curvature and connected sums

Abstract

Keywords

Cite

Comments

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