  We have recently proposed in \cite{Park:2014tia} the quantization of pure 4D
Einstein gravity through hypersurface foliation, and observed that the 4D
Einstein gravity becomes renormalizable once all (or most) of the unphysical
degrees of freedom are removed. In this work, we confirm this observation from
a more mathematical angle. In particular, we show that the physical state
condition arising from the shift vector constraint connects with the
requirement that the manifold admit "totally geodesic (TG) foliation". The TG
foliation, in turn, makes it possible to view the 4D manifold as abelian
fibration over a 3D base. Associating the abelian fibration with the 4D
diffeomorphism leads to reduction of the 4D manifold to 3D, thereby realizing
and generalizing the holography of 't Hooft.
