Infinitesimal derivative of the Bott class and the Schwarzian derivatives (Q1045958)

The Bott class is a secondary characteristic class of transversally holomorphic foliations defined in a manner similar to the Godbillon-Vey class. It varies smoothly under deformations of foliations. Its infinitesimal derivative exists and is given by a construction of Heitsch in the case of the trivial normal bundle. In this paper, the infinitesimal derivatives are defined in full generality and are calculated via the Schwarzian derivatives giving a generalization of the Maszczyk formula for the Godbillon-Vey class of real codimension-one foliations. This is further applied to the Fatou-Julia decomposition, in the sense of Ghys, Gomez-Mont and Saludes, to calculate the residue classes of transversal projective structures on the Fatou component.