Proof of the Verjovsky Conjecture

Abstract

In this paper we present a proof of the Verjovsky conjecture: Every codimension-one Anosov flow on a manifold of dimension greater than three is topologically equivalent to the suspension of a hyperbolic toral automorphism. In fact, the conjecture is derived from possible more general result that says that for every codimension-one volume-preserving Anosov flow on a manifold of dimension greater than three, a suitable time change guarantees that the stable and unstable sub-bundles are then jointly integrable.