SUBJECT
Riemann surfaces
lecture
master
3
Semesters 1-4
Autumn/Spring semester
Abstract definition, coverings, analytic continuation, homotopy, theorem of monodromy, universal covering, covering group, Dirichlet's problem, Perron's method, Green function, homology, residue theorem, uniformization theorem for simply connected Riemann surfaces.
Determining the Riemann surface from its covering group. Fundamental domain, fundamental polygon. Riemann surface of an analytic function, compact Riemann surfaces and complex algebraic curves.
O. Forster: Lectures on Riemann surfaces, GTM81, Springer-Verlag, 1981