  Restrictions are obtained on the topology of a compact divergence-free null
hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is
zero or satisfies some weaker conditions. This is done by showing that each
null hypersurface of this type can be used to construct a family of
three-dimensional Riemannian metrics which collapses with bounded curvature and
applying known results on the topology of manifolds which collapse. The result
is then applied to general relativity, where it implies a restriction on the
topology of smooth compact Cauchy horizons in spacetimes with various types of
reasonable matter content.
