An improved cosmic crystallography method to detect holonomies in flat
  spaces
  A new, improved version of a cosmic crystallography method for constraining
cosmic topology is introduced. Like the circles-in-the-sky method using CMB
data, we work in a thin, shell-like region containing plenty of objects. Two
pairs of objects (quadruplet) linked by a holonomy show a specific distribution
pattern, and three filters of \emph{separation, vectorial condition}, and
\emph{lifetime of objects} extract these quadruplets. Each object $P_i$ is
assigned an integer $s_i$, which is the number of candidate quadruplets
including $P_i$ as their members. Then an additional device of $s_i$-histogram
is used to extract topological ghosts, which tend to have high values of $s_i$.
In this paper we consider flat spaces with Euclidean geometry, and the filters
are designed to constrain their holonomies. As the second filter, we prepared
five types that are specialized for constraining specific holonomies: one for
translation, one for half-turn corkscrew motion and glide reflection, and three
for $n$-th turn corkscrew motion for $n=4, 3,$ and 6. {Every multiconnected
space has holonomies that are detected by at least one of these five filters.}
Our method is applied to the catalogs of toy quasars in flat $\Lambda$-CDM
universes whose typical sizes correspond to $z\sim 5$. With these simulations
our method is found to work quite well. {These are the situations in which
type-II pair crystallography methods are insensitive because of the tiny number
of ghosts. Moreover, in the flat cases, our method should be more sensitive
than the type-I pair (or, in general, $n$-tuplet) methods because of its
multifilter construction and its independence from $n$.}
