  We show that an orientable 3-dimensional manifold M admits a complete
riemannian metric of bounded geometry and uniformly pos- itive scalar curvature
if and only if there exists a finite collection F of spherical space-forms such
that M is a (possibly infinite) connected sum where each summand is
diffeomorphic to S2xS1 or to some mem- ber of F. This result generalises G.
Perelman's classification theorem for compact 3-manifolds of positive scalar
curvature. The main tool is a variant of Perelman's surgery construction for
Ricci flow.
