Atoroidal surface bundles
Geometric Topology
2026-05-04 v2 Group Theory
Abstract
We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes of purely pseudo-Anosov surface subgroups of mapping class groups of closed surfaces. This gives the first examples of compact atoroidal surface bundles over surfaces.
Cite
@article{arxiv.2405.12067,
title = {Atoroidal surface bundles},
author = {Autumn E. Kent and Christopher J. Leininger},
journal= {arXiv preprint arXiv:2405.12067},
year = {2026}
}
Comments
39 pages, 1 figure. Updated to incorporate referee comments. To appear in the Annals of Mathematics