Optimal positioning of tori with respect to an Anosov flow
Anosov flows on 3-manifolds are studied via their incompressible tori. A technical term is ``optimal position'' of such a torus, which essentially means that it is isotopic to a torus transverse to the flow outside finitely many closed orbits. Homotopic tori in optimal position are homotopic along the flow. A topological condition is given that guarantees that a torus can be isotoped to one in optimal position. If finitely many disjoint tori can separately be deformed to tori in optimal position then the latter can be chosen to be disjoint. An important role in the geometric analysis of a Birkhoff annulus in such an Anosov flow is played by ``lined up lozenges'' (chapelet de losanges - diamond shaped pieces chained up in a row), a subset in the orbit space of the universal cover of the 3-manifold by the canonical 1-dimensional foliation.
scientific article; zbMATH DE number 791087