507 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 508 R. L. BRYANT AND P. A. GRIFFITHS 6. Global results 6.1. A relation between ordinary and characteristic cohomology 6.2. J -homology 6.3. Moment conditions References The first assumption means t~at fa contains no functions-otherwise we may replace Xo by the subset, assumed to be a submanifold, defined by setting equal to zero all of the functions in fa. Neither assumption changes

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... set of n-dimensional integral manifolds. The very definition of an exterior differential system suggests that we consider the complex {n~, d} where Provisional Definition 1.1. The characteristic cohomology n; of the exterior differential system 50 is by definition the cohomology of the complex {n~, d} , n; = H{Q~, d}. Elements rp E n; are called characteristlc classes of 50.