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Flat space models with multiply connected topology, which have compactdimensions, are tested against the distribution of high-redshift ($z \geq 4$)quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions aresmaller in size than the observed universe, topological lensing occurs, inwhich multiple images of single objects (ghost images) are observed. We improveon the recently introduced method to identify ghost images by means offour-point statistics. Our method is valid for any of the 17 multiply connectedflat models, including nontoroial ones that are compactified by screw motionsor glide reflection. Applying the method to the data revealed one possible caseof topological lensing caused by sixth-turn screw motion, however, it isconsistent with the simply connected model by this test alone. Moreover,simulations suggest that we cannot exclude the other space models despite theabsence of their signatures. This uncertainty mainly originates from the patchycoverage of SDSS in the South Galactic cap, and the situation will be improvedby future wide-field spectroscopic surveys.

A search for nontoroidal topological lensing in the Sloan Digital Sky Survey quasar catalog