Abstract
We study the topology of codimension one taut foliations of closed orientable 3-manifolds which are smooth along the leaves. In particular, we focus on the lifts of these foliations to the universal cover, specifically when any set of leaves corresponding to nonseparable points in the leaf space can be totally ordered. We use the structure of branching in the lifted foliation to find conditions that ensure two nonseparable leaves are left invariant under the same covering translation. We also determine when the set of leaves nonseparable from a given leaf is finite up to the action of covering translations. The hypotheses for the results are satisfied by all Anosov foliations.
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