Microwave background anomalies motivate further searches for cosmic topology. For manifolds other than the simple 3-torus, existing searches allow the shortest distance around the Universe to be much less than the distance to the horizon. Yet, to explain anomalies, the shortest distance through us is likely to just exceed the horizon size. While galaxy and 21cm surveys are potentially more powerful, a more thorough microwave background search is merited as previous ones considered only a subset of topologies and of their parameter spaces. Current limits on topology are much weaker than generally understood.
7 pages, 3 figures. v2: Shortened version; corrected Fig. 1; updated discussion to account for changes in Fig. 1; expanded discussion on implications of CMB anomalies; added discussion on large-scale structure surveys