Taut foliations, leftorders, and pseudoAnosov mapping tori
Abstract
For a large class of 3manifolds with taut foliations, we construct an action of $\pi_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms which captures the transverse geometry of the leaves. This action is complementary to Thurston's universal circle. Applications include the leftorderability 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 nonLspace rational homology spheres in the HodgsonWeeks census of small closed hyperbolic 3manifolds.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.07706
 Bibcode:
 2020arXiv200607706Z
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 27 pages, 11 figures