  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.
