TOPOLOGICAL CENSORSHIP

All three-manifolds are known to occur as Cauchy surfaces of asymptoti cally flat vacuum spacetimes and of spacetimes with positive-energy so urces. We prove here the conjecture that general relativity does not a llow an observer to probe the topology of spacetime: Any topological s tructure collapses too quickly to allow light to traverse it. More pre cisely, in a globally hyperbolic, asymptotically flat space-time satis fying the null energy condition, every causal curve from J- to J+ is h omotopic to a topologically trivial curve from J- to J+.