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

Zung, Jonathan

doi:10.2140/gt.2024.28.4191

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

Jonathan Zung

Geometry & Topology 28 (2024) 4191–4232

DOI: 10.2140/gt.2024.28.4191

Abstract

For a large class of $3$ –manifolds with taut foliations, we construct an action of $π_{1} (M)$ 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.

Keywords

orderable groups, taut foliations, pseudo-Anosov flows

Mathematical Subject Classification

Primary: 20F60, 37C85, 57R30

References

Publication

Received: 6 July 2020

Revised: 27 June 2023

Accepted: 13 July 2023

Published: 27 December 2024

Proposed: David Gabai

Seconded: Ciprian Manolescu, Cameron Gordon

Authors

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

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Volume 28, issue 9 (2024)