JP Journal of Geometry and Topology
Volume 7, Issue 1, Pages 131 - 157
(March 2007)
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DIFFERENTIAL COMPLEXES WITH NONSMOOTHABLE COHOMOLOGY:OBSTRUCTIONS TO DE RHAM’S THEOREM
Tejinder S. Neelon (U.S.A.)
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Abstract:
Given a locally integrable structure 
(e.g. a CR structure) on a smooth manifold 
there is an associated differential complex of 
differential  -forms
and an associated differential complex of -currents.
The cohomology of a differential complex of
-currents is said to
be smoothable if it is isomorphic to
the cohomology of the corresponding complex of 
differential
 -forms. By the de
Rham theorem, the cohomology of de Rham complex of currents on a real manifold
and the cohomology of the  -complex
of  -currents on a
complex manifold are both smoothable. The necessary conditions for the
smoothability of differential complexes associated with locally integrable
structures are studied. The results and methods are similar to the ones for the
vanishing of cohomology in Cordaro-Trèves [2] and Cordaro-Hounie [4]. |
| Keywords and phrases: differential complexes, currents and differential forms, de Rham theorem, smoothable cohomology, complex vector fields, locally integrable structures. |
| Communicated by Yasuo Matsushita |
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