A search for nontoroidal topological lensing in the Sloan Digital Sky
  Survey quasar catalog
  Flat space models with multiply connected topology, which have compact
dimensions, are tested against the distribution of high-redshift ($z \geq 4$)
quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are
smaller in size than the observed universe, topological lensing occurs, in
which multiple images of single objects (ghost images) are observed. We improve
on the recently introduced method to identify ghost images by means of
four-point statistics. Our method is valid for any of the 17 multiply connected
flat models, including nontoroial ones that are compactified by screw motions
or glide reflection. Applying the method to the data revealed one possible case
of topological lensing caused by sixth-turn screw motion, however, it is
consistent with the simply connected model by this test alone. Moreover,
simulations suggest that we cannot exclude the other space models despite the
absence of their signatures. This uncertainty mainly originates from the patchy
coverage of SDSS in the South Galactic cap, and the situation will be improved
by future wide-field spectroscopic surveys.
