Positive scalar curvature and connected sums

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.

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