🚀 go-pugleaf

I am wondering if anyone has ever given an exposition of the
basic theory of Riemann surfaces that systematically did everything
on the universal covering space.  The idea would be that having
global coordinates would allow all objects such as differentials
of various sorts to be viewed as functions with appropriate
transformation properties, and theorems like Riemann-Roch, Serre
Duality, Abel-Jacobi might be accessible, in some guise, to readers
with only a basic knowledge of complex variables, but no significant
background in topology, sheaves, cohomology and the like.  I am
especially thinking here of compact Riemann surfaces of genus greater
than 2.

If no such exposition exists, in part, or in whole, I am interested
in opinions on what parts of the theory would be awkward from this
point of view.

David Feldman