Viktor Chueshev (Kemerovo State University, Russia) with Alena Kazantseva
  Vector bundle of abelian differentials over Teichmuller spaces of surfaces with punctures.

Function theory on compact Riemann surfaces essentially differs from function theory on finite Riemann surfaces even for class univalent meromorphic functions and abelian differentials.

In this article we continuable construction the general theory functions on finite Riemann surfaces for meromorphic functions and abelian differentials. We proved theorem about fiber isomorphism for holomorphic vector bundles and n!-sheeted holomorphic mappings over Teichmuller spaces.