Spikes in cosmic crystallography II: topological signature of compact flatuniverses

We study the topological signature of euclidean isometries in pair separati ons histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing th e noise of individual PSHs using mean pair separations histograms we show h ow to distinguish between topological and statistical spikes. We report res ults of simulations that evince that topological spikes are not enough to d istinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSHs corresponding to euclidean small universes. We also show how to ev ince the topological signature due to non-translational isometries. (C) 200 0 Published by Elsevier Science B.V.