On the characteristic classes of subfoliations (Q1105876)

A subfoliation is a pair \((F_ 1,F_ 2)\) of foliations \(F_ i\) such that \(F_ 2\subset F_ 1\). A theory of secondary characteristic classes for subfoliations has been initiated by \textit{B. L. Feigin} [Funkts. Anal. Prilozh. 9, No. 4, 49--56 (1975; Zbl 0328.57008)], the reviewer and \textit{X. Masa} [Ann. Inst. Fourier Grenoble 31, No. 2, 61--86 (1981; Zbl 0442.57009)] and \textit{J. M. Carballés} [Ann. Inst. Fourier 34, No. 3, 219--245 (1984; Zbl 0519.57022)]. In the paper under review the author computes the cohomology algebra \(H(W(g,H)_ I)\), domain for the characteristic homomorphism of a subfoliation. He also studies some properties of a subfoliation and gives a geometric interpretation for certain characteristic classes, in particular for the Godbillon-Vey classes of a subfoliation. The nontriviality of this study is shown by constructing examples of subfoliations with nontrivial Godbillon-Vey classes.