A remark on the Bott class
In several real and complex situations the geometric properties of the characteristic classes of foliations are not yet clear. The author considers the imaginary part \(\xi _q\) of the Bott class. An associated cocycle for \(\xi _q\) in the Čech-de Rham complex is defined. The class \(\xi _q\) reflects how the local holonomy maps expand and rotate transverse discs. The vanishing of this class for foliations having a transverse volume form, or for transversely complex affine foliations, is given. The author shows also that the class \(\xi _q\) has a certain relationship with a group cocycle.
scientific article; zbMATH DE number 1796101
scientific article