Stein manifolds on which the strong Poincaré problem can be solved
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- by Robert Ephraim PDF
- Proc. Amer. Math. Soc. 70 (1978), 136-138 Request permission
Abstract:
Let M be a Stein manifold. Suppose every meromorphic function on M may be written as the quotient of two holomorphic functions which are pointwise relatively prime at every point of M. Then it will be shown that ${H^2}(M,Z) = 0$. Thus, the solvability of the Strong Poincaré Problem is equivalent to the vanishing of the second integral cohomology, which in turn is equivalent to the solvability of Cousin II, all on a Stein manifold M. This closes a gap in the classically known theory.References
- H. G. Dales, The ring of holomorphic functions on a Stein compact set as a unique factorization domain, Proc. Amer. Math. Soc. 44 (1974), 88–92. MR 333245, DOI 10.1090/S0002-9939-1974-0333245-4
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 136-138
- MSC: Primary 32E10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0481104-2
- MathSciNet review: 0481104