Abstract
A proof that homology groups Hk(x; бX) of a complex analytic space X, countable at infinity and locally smoothly contractible, with coefficients in the lattice bundle бX, are canonically isomorphic to the corresponding homology groups
of the finite complex of analytic differential forms
with the exterior differential d” as a coboundary operator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J.-P. Serre, “Géométrie algébrique et géométrie analytique,” Ann. Inst. Fourier,6, 1–42 (1955–1956).
J.-P. Serre, Coherent Algebraic Bundles, in: Fibered Spaces and Their Applications [Russian translation], Moscow (1958).
R. Godement, Algebraic Topology and Bundle Theory [Russian translation], Moscow (1961).
P. Dolbeault, “Formes différentielles et cohomologie sur une variété analytique complexe,” Ann. of Math.,64, No. 1, 83–130 (1956).
H. J. Reiffen, “Das Lemma von Poincaré für holomorphe Differentialformen auf complexen Räumen, Math. Zeitschr.,101, No. 4, 269–284 (1967).
H. Cartan, “Variétés analytiques réeles et variétés analytiques complexes,” Bull. Soc. Math. France,85, No. 1, 77–99 (1957).
H. Grauert, “On Levi's problem and enclosures of substantially analytical diversity,” Matematika,4, 3, 29–40 (1960).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 569–573, May, 1971.
Rights and permissions
About this article
Cite this article
Golovin, V.D. Cohomologies and analytic differential forms. Mathematical Notes of the Academy of Sciences of the USSR 9, 330–332 (1971). https://doi.org/10.1007/BF01094361
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01094361