Notes on 'Infinitesimal derivative of the Bott class and the Schwarzian derivatives'

Abstract

The derivatives of the Bott class and those of the Godbillon-Vey class with respect to infinitesimal deformations of foliations, called infinitesimal derivatives, are known to be represented by a formula in the projective Schwarzian derivatives of holonomies [3], [1]. It is recently shown that these infinitesimal derivatives are represented by means of coefficients of transverse Thomas-Whitehead projective connections [2]. We will show that the formula can be also deduced from the latter representation.