Projectively Invariant Cocycles of Holomorphic Vector Fields on an Open Riemann Surface
Abstract
Description
Let $Σ$ be an open Riemann surface and $Hol (Σ)$ be the Lie algebra of holomorphic vector fields on $Σ.$ We fix a projective structure (i.e. a local $SL_2(C)-$structure) on $Σ.$ We calculate the first group of cohomology of $Hol(Σ)$ with coefficients in the space of linear holomorphic operators acting on tensor densities, vanishing on the Lie algebra $SL_2 (C).$ The result is independant on the choice of the projective structure. We give explicit formulae of 1-cocycles generating this cohomology group.
8 pages, no figures, Latex2e
8 pages, no figures, Latex2e