The Godbillon-Vey characteristic class

Andrei Teleman (1)

1 UniBuc - University of Bucharest

Let M be a (not necessarily paracompact) smooth manifold, F a 1-codimensional foliation on it, {U_i} an open cover of M and ω_i one-forms defining F|_{U_i}. The author defines a cohomology class in H^∗(Ω^∗) (the hypercohomology of the de Rham sheaf complex of M) and proves that in the paracompact case it coincides with the Godbillon-Vey class. In the paracompact case the new definition can be made even simpler and one obtains a cohomology class in the real Čech cohomology of M. No Riemannian metrics or connections are used. The holomorphic and algebraic cases are also discussed.

Mots clés: foliation; Godbillon-Vey class

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Andrei Teleman. The Godbillon-Vey characteristic class. Studii şi Cercetări Matematice, 1985, 37 (5), pp.472-475. ⟨hal-00881782⟩