Local observations can only measure the geometry of the universe.
We need to look out beyond our own fundamental domain to begin to see the effects of topology. That is, if we randomly select a point in such a manifold, this is the most probable value for the conformal distance to our nearest copy. In a matter dominated universe, the redshift of an object is related to the conformal distance by where is the conformal lookback time, and is the present conformal time. For an universe, and the nearest image of ourselves is likely to lie between a redshift of 0.9 and 2.9. Similarly, if , we find and the nearest copy will typically lie between a redshift of 1.0 and 3.8.