Verjovsky's conjecture on codimension-one Anosov flows

Let $M$ be a closed manifold of dimension greater than three, and let $F$ be a codimension-one Anosov flow on $M$. Two flows are topologically equivalent if a homeomorphism maps their orbits homeomorphically while preserving orbit orientation. A suspension flow is the flow obtained from a diffeomorphism by identifying the ends of its mapping cylinder; a hyperbolic toral automorphism is an automorphism of a torus induced by an integer matrix with no eigenvalues of modulus one.

Verjovsky's conjecture. Any codimension-one Anosov flow on a closed manifold of dimension greater than three is topologically equivalent to the suspension flow of a hyperbolic toral automorphism.

The conjecture concerns the classification of codimension-one Anosov flows up to topological equivalence. The source presents a proof of the conjecture, so its resolution should be checked against the paper's arguments.