Localization and residue of the Bott class

The Bott class of transversely holomorphic foliations is studied. We first introduce a formula which relates the Bott class and the Godbillon–Vey class. Then a ‘localizable part’ of the Bott class is defined. It is indeed localizable and written in terms of the Godbillon measure studied by Heitsch and Hurder. The above-mentioned formula is reviewed in terms of localizable parts. Finally, complex codimension-one foliations are considered. A version of residue is introduced and it is shown that the Bott class is ‘localized’ near the Julia set in the sense of Ghys–Gomez-Mont–Saludes. Some examples of calculation of the residue are presented.