Residues and secondary classes for subfoliations (Q1325951)

We present a theory of residues for subfoliations and relate these residues to the secondary characteristic classes for subfoliations. The method used is a generalization of Heitsch's theory of residues for foliations. We compute examples which show that certain universal secondary characteristic classes for subfoliations of codimension \((q_ 1,q_ 2)\) vary linearly independently. These results show that the homology group \(H_{2q_ 2+ 2}(B\Gamma_{(q_ 1,q_ 2)};\mathbb{Z})\) of the Haefliger classifying space \(B\Gamma_{(q_ 1,q_ 2)}\) for subfoliations of codimension \((q_ 1,q_ 2)\) admits an epimorphism onto Euclidean space. The classes considered do not belong to the subalgebra of \(H^*(B\Gamma_{(q_ 1,q_ 2)}; \mathbb{R})\) generated by the union of the universal characteristic classes for foliations of codimension \(q_ 1\) and \(q_ 2\) respectively.