On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces
The continuous cohomology theory of the Lie algebra of complex analytic vector fields on an open Riemann surface is studied. We show that the cohomology group with coefficients in the -module of germs of complex analytic tensor fields on the product space decomposes into the global part derived from the homology of and the local part coming from the coefficients.