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arxiv: 0711.0227 · v1 · submitted 2007-11-02 · 🧮 math.CV · math.AP· math.AT

The Poincare lemma and local embeddability

Judith Brinkschulte , C. Denson Hill , Mauro Nacinovich This is my paper
classification 🧮 math.CV math.APmath.AT
keywords lemmaabstractembeddabilityformslocalmanifoldspoincarevalidity
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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.

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