A MARTENS-TYPE THEOREM IN THE CONTEXTOF COHOMOLOGY OF RIEMANN SURFACES

摘要

A holomorphic map between closed Riemann surfacesis completely determined by the induced homomorphism of the first homology groupswith integer coefficients. This is a consequence of Martens' theorem proven in [6]. In this paper,we study holomorphic maps of closed Riemann surfaces in the context of cohomology and extend Martens' theorem.