  The set of one dimensional lowest energy eigenspaces used to construct the
overlap induces a two form on gauge orbit space which is the locally exact curl
of Berry's connection. If anomalies do not cancel, examples of two dimensional
closed sub-manifolds of orbit space are produced over which the integral of the
above two form does not vanish. Based on these observations, a natural
definition of covariant currents is obtained, a simple way to calculate chiral
anomalies on the lattice is found, and indications for how to construct an
ideal regularization of chiral gauge theories are seen to emerge.
