A relation between the topological invariance of the Godbillon-Vey invariant and the Differentiability of Anosov foliations. (English) Zbl 0653.57018

Mitsumatsu, Yoshihiko

Foliations, Proc. Symp., Tokyo 1983, Adv. Stud. Pure Math. 5, 159-167 (1985).

[For the entire collection see Zbl 0627.00017.]
In this paper, we study Anosov’s unstable foliations of the geodesic flows of negatively curved surfaces to show some relation between the topological invariance of the Godbillon-Vey invariant of codimension one \(C^ 2\)-foliations and the differentiability of such foliations. We treat foliations only on closed oriented 3-manifolds, so that we study the Godbillon-Vey number which is the value of the Godbillon-Vey invariant on the fundamental class of the manifold.

MSC:

57R30	Foliations in differential topology; geometric theory
37D99	Dynamical systems with hyperbolic behavior

Keywords:

differentiability of foliations; unstable foliations of the geodesic flows of negatively curved surfaces; topological invariance of the Godbillon-Vey invariant; Godbillon-Vey number

Citations:

Zbl 0627.00017