Taut foliations, left orders, and pseudo-Anosov mapping tori

For a large class of 3-manifolds with taut foliations, we construct an action of 1 .M / on R by orientationpreserving homeomorphisms which captures the transverse geometry of the leaves.This action is complementary to Thurston's universal circle.Applications include the left-orderability of the fundamental groups of every nontrivial surgery on the figure-eight knot.Our techniques also apply to at least 2598 manifolds representing 44.7% of the non-L-space rational homology spheres in the Hodgson-Weeks census of small closed hyperbolic 3-manifolds.20F60, 37C85, 57R30 1. Introduction 4191 2. Notation and conventions 4194 3. Foliations on surgeries on pseudo-Anosov mapping tori 4197 4.