All 3-manifolds are known to occur as Cauchy surfaces of asymptotically
flat vacuum spacetimes and of spacetimes with positive-energy sources.
We prove here the conjecture that general relativity does not allow an
observer to probe the topology of spacetime: any topological structure
collapses too quickly to allow light to traverse it. More precisely,
in a globally hyperbolic, asymptotically flat spacetime satisfying the
null energy condition, every causal geodesic from 
to
is homotopic to a topologically trivial curve from
to 
.
