Toroidal 3-manifolds have circularly orderable fundamental groups
Geometric Topology
2026-07-12 v1
Abstract
In this article we prove that toroidal 3-manifolds have circularly-orderable fundamental groups by showing that they admit finite cyclic covers with left-orderable fundamental groups. These covers are also not L-spaces and often admit co-orientable taut foliations, as predicted by the L-space conjecture. As a consequence, we verify a conjecture of Ba and Clay, which characterises graph manifolds with circularly-orderable fundamental groups.
Cite
@article{arxiv.2607.10529,
title = {Toroidal 3-manifolds have circularly orderable fundamental groups},
author = {Steven Boyer and Cameron McA. Gordon and Ying Hu},
journal= {arXiv preprint arXiv:2607.10529},
year = {2026}
}
Comments
v1: 12 pages, no figures