On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects

We present a method to constrain cosmic topology from the distribution of astronomical objects projected on the celestial sphere. This is an extension of the 3D method introduced in Fujii & Yoshii (2011) that is to search for a pair of pairs of observed objects (quadruplet) linked by a holonomy, i.e., the method we present here is to search for a pair of celestial sphere $n$-tuplets for $n \geq 3$. We find, however, that this method is impractical to apply in realistic situations due to the small signal to noise ratio. We conclude therefore that it is unrealistic to constrain the topology of the Universe from the celestial distribution, and the 3D catalogs are necessary for the purpose.