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.
Dans cet article nous étudions la cohomologie continue de l’algèbre de Lie des champs de vecteurs analytiques complexes sur une surface de Riemann ouverte . Nous montrons que le groupe de cohomologie à coefficients dans le -module des germes de champs de tenseurs analytiques complexes sur le produit se décompose en la partie globale dérivée de l’homologie de et la partie locale provenant des coefficients.
@article{AIF_1993__43_3_655_0, author = {Kawazumi, Nariya}, title = {On the complex analytic {Gel'fand-Fuks} cohomology of open {Riemann} surfaces}, journal = {Annales de l'Institut Fourier}, pages = {655--712}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {43}, number = {3}, year = {1993}, doi = {10.5802/aif.1351}, mrnumber = {94i:58211}, zbl = {0782.57019}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1351/} }
TY - JOUR AU - Kawazumi, Nariya TI - On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces JO - Annales de l'Institut Fourier PY - 1993 SP - 655 EP - 712 VL - 43 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.1351/ DO - 10.5802/aif.1351 LA - en ID - AIF_1993__43_3_655_0 ER -
%0 Journal Article %A Kawazumi, Nariya %T On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces %J Annales de l'Institut Fourier %D 1993 %P 655-712 %V 43 %N 3 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.1351/ %R 10.5802/aif.1351 %G en %F AIF_1993__43_3_655_0
Kawazumi, Nariya. On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces. Annales de l'Institut Fourier, Volume 43 (1993) no. 3, pp. 655-712. doi : 10.5802/aif.1351. http://archive.numdam.org/articles/10.5802/aif.1351/
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