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Proceedings of the American Mathematical Society

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On cohomology groups of certain subcomplexes of Dolbeault complexes


Author: Shaw Mong
Journal: Proc. Amer. Math. Soc. 38 (1973), 632-636
MSC: Primary 58A10; Secondary 32C30, 32C35
MathSciNet review: 0314080
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Abstract: The paper first shows that for a path connected topological group acting analytically on a complex manifold $ M$, the induced action on the cohomology groups of antiholomorphic forms on $ M$ is trivial. By the same method it then shows that the cohomology groups of complex $ \{ \ker {\partial ^{p,\ast}}\} $ can be injected into the Dolbeault cohomology groups.


References [Enhancements On Off] (What's this?)

  • [1] A. Aeppli, On the cohomology structure of Stein manifolds, Proc. Conf. Complex Analysis (Minneapolis, Minn., 1964) Springer, Berlin, 1965, pp. 58–70. MR 0221536
  • [2] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0314080-9
Keywords: $ G$-manifolds, differential forms, antiholomorphic forms, DeRham complexes, Dolbeault complexes, cohomology groups
Article copyright: © Copyright 1973 American Mathematical Society