Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Stein manifolds on which the strong Poincaré problem can be solved


Author: Robert Ephraim
Journal: Proc. Amer. Math. Soc. 70 (1978), 136-138
MSC: Primary 32E10
MathSciNet review: 0481104
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32E10

Retrieve articles in all journals with MSC: 32E10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0481104-2
PII: S 0002-9939(1978)0481104-2
Keywords: Stein manifold, Strong Poincaré Problem, meromorphic function, positive divisors, Cousin II, integral cohomology
Article copyright: © Copyright 1978 American Mathematical Society