On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces

Kawazumi, Nariya

Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 655-712.

Dans cet article nous étudions la cohomologie continue de l’algèbre de Lie $L\left(M\right)$ des champs de vecteurs analytiques complexes sur une surface de Riemann ouverte $M$. Nous montrons que le groupe de cohomologie à coefficients dans le $L\left(M\right)$-module des germes de champs de tenseurs analytiques complexes sur le produit $M^n$ se décompose en la partie globale dérivée de l’homologie de $M$ et la partie locale provenant des coefficients.

The continuous cohomology theory of the Lie algebra $L\left(M\right)$ of complex analytic vector fields on an open Riemann surface $M$ is studied. We show that the cohomology group with coefficients in the $L\left(M\right)$-module of germs of complex analytic tensor fields on the product space $M^n$ decomposes into the global part derived from the homology of $M$ and the local part coming from the coefficients.

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