ON THE LINEAR INDEPENDENCE OF CERTAIN COHOMOLOGY CLASSES IN THE CLASSIFYING SPACE FOR SUBFOLIATIONS

The purpose of this paper is to establish the linear independence of certain cohomology classes in the Haefliger classifying space B-GAMMA(q1, q2) for subfoliations of codimension (q1, q2). The classes considered are of secondary type, not belonging to the subalgebra of H(B-GAMMA(q1, q2), R) generated by the union of the universal characteristic classes for foliations of codimension q1 and q2 respectively, and are elements of the kernel of the canonical homomorphism H(B-GAMMA(q1, q2), R) --> H(B-GAMMA(q1) x B-GAMMA(d), R) with d = q2 - q1 > 0.