  Morphology of the complex HI gas distribution can be quantified by statistics
like the Minkowski functionals, and can provide a way to statistically study
the large scale structure in the HI maps both at low redshifts, and during the
epoch of reionization (EoR). At low redshifts, the 21cm emission traces the
underlying matter distribution. Topology of the HI gas distribution, as
measured by the genus, could be used as a "standard ruler". This enables the
determination of distance-redshift relation and also the discrimination of
various models of dark energy and of modified gravity. The topological analysis
is also sensitive to certain primordial non-Gaussian features. Compared with
two-point statistics, the topological statistics are more robust against the
nonlinear gravitational evolution, bias, and redshift-space distortion. The HI
intensity map observation naturally avoids the sparse sampling distortion,
which is an important systematic in optical galaxy survey. The large cosmic
volume accessible to SKA would provide unprecedented accuracy using such a
measurement... [abridged]
