  Let us consider a generic n-dimensional subbundle V of the tangent bundle TM
on some given manifold M. Given V one can define different degeneracy loci
S_r(CV), r=(r_1<= r_2<= r_3<=...<=r_k) on M consisting of all points x in M for
which the dimension of the subspace V^j(x) in TM(x) spanned by all length <= j
commutators of vector fields tangent to V at x is less than or equal to r_j. We
calculate 'explicitly' the cohomology classes dual to S_r(V) using
determinantal formulas due to W.Fulton and the expression for the Chern classes
of the associated bundle of free Lie algebras in terms of the Chern classes of
V itself.
