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For a large class of 3-manifolds with taut foliations, we construct an actionof $\pi_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms whichcaptures the transverse geometry of the leaves. This action is complementary toThurston's universal circle. Applications include the left-orderability of thefundamental groups of every non-trivial surgery on the figure eight knot. Ourtechniques also apply to at least 2598 manifolds representing 44.7% of thenon-L-space rational homology spheres in the Hodgson-Weeks census of smallclosed hyperbolic 3-manifolds.

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