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

Zung, Jonathan¹

¹ Department of Mathematics, Princeton University, Princeton, NJ, United States, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 28 (2024) no. 9, pp. 4191-4232.

Résumé

For a large class of $3$–manifolds with taut foliations, we construct an action of ${\pi }_1(M)$ on $ℝ$ by orientation-preserving 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.

Détail

DOI : 10.2140/gt.2024.28.4191

Keywords: orderable groups, taut foliations, pseudo-Anosov flows

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