Projectively Invariant Cocycles of Holomorphic Vector Fields on an Open Riemann Surface
Abstract
Let be an open Riemann surface and Hol () be the Lie algebra of holomorphic vector fields on . We fix a projective structure (i.e. a local SL2(C)-structure) on . We calculate the first group of cohomology of Hol() with coefficients in the space of linear holomorphic operators acting on tensor densities, vanishing on the Lie algebra SL2 (C). The result is independant on the choice of the projective structure. We give explicit formulae of 1-cocycles generating this cohomology group.
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