Toroidal 3-manifolds have circularly orderable fundamental groups

Steven Boyer; Cameron McA. Gordon; Ying Hu

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arXiv · 2607.10529

Toroidal 3-manifolds have circularly orderable fundamental groups

Steven Boyer·Cameron McA. Gordon·Ying Hu

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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.

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Steven Boyer, Cameron McA. Gordon, Ying Hu. 2026-07-12. Toroidal 3-manifolds have circularly orderable fundamental groups. https://arxiv.org/abs/2607.10529

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