  I argue that the first-order formalism recently found to describe classical
2+1-Gravity with matter, is also able to include higher topologies. The present
gauge, which is conformal with vanishing York time, is characterized by an
analytic mapping from single-valued coordinates to Minkowskian ones. In the
torus case, this mapping is based on four square-root branch points, whose
location is related to the modulus, which has a well defined time dependence.
In the general case, it is connected with the hyperelliptic representation of
Riemann surfaces.
