  We show that the existence of an embedded compact, boundaryless hypersurface
S of strictly positive mean curvature in a noncompact, connected, complete
Riemannian n-manifold N of nonnegative Ricci curvature implies that the
homomorphism between the fundamental groups of S and N induced by the inclusion
is surjective, provided only that N - S has two connected components, one of
which has noncompact closure and trivial homotopy relative to S. The idea of
the proof is to view N as a spacelike hypersurface in a suitable Lorentz
manifold and then apply a recent version of certain classic results by Gannon
and Lee on the topology of spacetimes. As an application, we show that if N is
asymptotically flat, then it has only one end, and N is simply connected for n
larger than 3.
