Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [M. G. Eastwood, S. G. Gindikin and H.-W. Wong, J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes a version of Čech cohomology based on a smoothly parametrized Stein cover. The idea of this language is that, usually, there are only infinite Stein coverings of the complex manifold in question but, often, we can find natural Stein coverings parametrized by an auxiliary smooth manifold. Under these circumstances, it is unnatural to work with classical Čech cohomology. Instead, it is possible to construct the !
@article{701706,
title = {Nonclassical descriptions of analytic cohomology},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2003},
pages = {[67]-72},
mrnumber = {MR1982434},
zbl = {1028.32004},
url = {http://dml.mathdoc.fr/item/701706}
}
Bailey, Toby N.; Eastwood, Michael G.; Gindikin, Simon G. Nonclassical descriptions of analytic cohomology, dans Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books, (2003), pp. [67]-72. http://gdmltest.u-ga.fr/item/701706/