## The Poincare lemma and local embeddability

##### Authors
Brinkschulte, Judith
Hill, C. Denson
Nacinovich, Mauro
##### Description
For pseudoconvex abstract CR manifolds, the validity of the Poincare Lemma for (0,1) forms implies local embeddability in C^N. The two properties are equivalent for hypersurfaces of real dimension > or = 5. As a corollary we obtain a criterion for the non validity of the Poicare Lemma for (0,1) forms for a large class of abstract CR manifolds of CR codimension larger than one.
##### Keywords
Mathematics - Complex Variables, Mathematics - Analysis of PDEs, Mathematics - Algebraic Topology, 32V30, 35N10