Lewy's Example - Significance For CR Manifolds

Significance For CR Manifolds

A CR manifold comes equipped with a chain complex of differential operators, formally similar to the Dolbeault complex on a complex manifold, called the -complex. The Dolbeault complex admits a version of the Poincaré lemma. In the language of sheaves, this means that the Dolbeault complex is exact. The Lewy example, however, shows that the -complex is almost never exact.