The Poincare lemma and local embeddability

Judith Brinkschulte; C. Denson Hill; Mauro Nacinovich

The Poincare lemma and local embeddability

Complex Variables 2007-11-06 v1 Analysis of PDEs Algebraic Topology

Authors: Judith Brinkschulte , C. Denson Hill , Mauro Nacinovich

Abstract

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.

Cite

@article{arxiv.0711.0227,
  title  = {The Poincare lemma and local embeddability},
  author = {Judith Brinkschulte and C. Denson Hill and Mauro Nacinovich},
  journal= {arXiv preprint arXiv:0711.0227},
  year   = {2007}
}