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

Nariya Kawazumi — 1993

Annales de l'institut Fourier

The continuous cohomology theory of the Lie algebra $L (M)$ of complex analytic vector fields on an open Riemann surface $M$ is studied. We show that the cohomology group with coefficients in the $L (M)$ -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.

[unknown]

Nariya Kawazumi; Yusuke Kuno

Annales de l’institut Fourier

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