The Godbillon-Vey invariant of a transversely homogeneous foliation

Source abstract

A real projective foliation is a foliation F \mathfrak {F} with a system of local coordinates transverse to F \mathfrak {F} modelled on R P 1 {\mathbf {R}}{P^1} (so that the coordinate changes are real linear fractional transformations). Given a closed manifold M M , there is but a finite set of values in H 3 ( M ; R ) {H^3}(M;{\mathbf {R}}) which the Godbillon-Vey invariant of such foliations may assume. A bound on the possible values, in terms of the fundamental group, is computed. For M M an oriented circle bundle over a surface, this finite set is explicitly computed.