  We show that the topological central charge of a topological phase can be
directly accessed from the ground-state wavefunctions for a system on a surface
as a Berry curvature produced by adiabatic variation of the metric on the
surface, at least up to addition of another topological invariant that arises
in some cases. For trial wavefunctions that are given by conformal blocks
(chiral correlation functions) in a conformal field theory (CFT), we carry out
this calculation analytically, using the hypothesis of generalized screening.
The topological central charge is found to be that of the underlying CFT used
in the construction, as expected. The calculation makes use of the
gravitational anomaly in the chiral CFT. It is also shown that the Hall
conductivity can be obtained in an analogous way from the U($1$) gauge anomaly.
