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Given a distribution of k-planes on a manifold, consider the degeneration locus I consisting of points where the distribution has Lie-bracket growth vector less than or equal I, a xed integer vector. We calculate the characteristic classes associated to the I for a generic two-plane distribution on a four-manifold. 1. Results and Background. 1.1. Generalities, Setting and Results. A distribution D of k-planes on an n-dimensional manifold Q can be thought of as either a subbundle DTQ of the tangent bundle or as a locally free sheaf of smooth vector elds. We use the same notation for both. Write D 2 = D +[ D ;D] and more generally D j+1 = D j +[ D ;D j ]. These are sheaves of modules of vector elds (over the ring of smooth functions). We are interested in distributions such that for r large enough we obtain all vector elds by this procedure: D r = T

Characteristic classes for the degenerations of two-plane fields in four dimensions