Characteristic classes of transversely homogeneous foliations

Abstract

The foliations studied in this paper have transverse geometry modeled on a homogeneous space G / H G/H with transition functions given by the left action of G G . It is shown that the characteristic classes for such a foliation are determined by invariants of a certain flat bundle. This is used to prove that when G G is semisimple, the characteristic classes are rigid under smooth deformations, extending work of Brooks, Goldman and Heitsch.