Local exactness

in a class of differential complexes

Authors:
Sagun Chanillo and François Treves

Journal:
J. Amer. Math. Soc. **10** (1997), 393-426

MSC (1991):
Primary 35A07, 35F05

DOI:
https://doi.org/10.1090/S0894-0347-97-00231-2

MathSciNet review:
1423030

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Abstract | References | Similar Articles | Additional Information

Abstract: The article studies the local exactness at level in the differential complex defined by commuting, linearly independent real-analytic complex vector fields in independent variables. Locally the system admits a first integral , i.e., a complex function such that and . The germs of the ``level sets'' of , the sets , are invariants of the structure. It is proved that the vanishing of the (reduced) singular homology, in dimension , of these level sets is sufficient for local exactness at the level . The condition was already known to be necessary.

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Additional Information

**Sagun Chanillo**

Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Email:
chanillo@math.rutgers.edu

**François Treves**

Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Email:
treves@math.rutgers.edu

DOI:
https://doi.org/10.1090/S0894-0347-97-00231-2

Keywords:
Differential complex,
local solvability,
singular homology,
subanalytic sets

Received by editor(s):
May 17, 1996

Received by editor(s) in revised form:
November 11, 1996

Additional Notes:
The first author was partially supported by NSF Grant DMS-9401782, and the second author by NSF Grant DMS-9201980

Article copyright:
© Copyright 1997
American Mathematical Society