Anomalous large-angle cosmic microwave background anisotropies motivate
further searches for cosmic topology. We demonstrate that for generic
topologies of spatially flat spacetimes, off-diagonal correlations between
microwave background harmonic coefficients over a wide range of scales encode
significant topological information, even if the topology scale substantially
exceeds the diameter of the observable Universe. Observational searches have so
far considered only a small subset of testable topologies, and current limits
on the topology scale are much weaker than generally understood.
