Cones of foliations almost without holonomy

Abstract

On sutured 3-manifolds $M$, we classify taut foliations almost without holonomy up to isotopy. We assume that the compact leaves lie in $\partial M$. The classification is given by finitely many convex, polyhedral cones in $H^{1}(M;\mathbb{R})$ which have disjoint interiors. The classes in the interiors of these cones determine the isotopy classes. This work relies heavily on the Handel–Miller classification of the isotopy classes of endperiodic surface automorphisms. While the Handel–Miller theory was not published by the originators, the authors have given a complete account elsewhere.