Circular-orderability of 3-manifold groups

Ba, Idrissa; Clay, Adam

doi:10.2140/agt.2025.25.791

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Circular-orderability of $3$-manifold groups

Idrissa Ba and Adam Clay

Algebraic & Geometric Topology 25 (2025) 791–825

DOI: 10.2140/agt.2025.25.791

Abstract

We initiate the study of circular-orderability of $3$ -manifold groups, motivated by the L-space conjecture. We show that a compact, connected, $ℙ^{2}$ -irreducible $3$ -manifold has a circularly orderable fundamental group if and only if there exists a finite cyclic cover with left-orderable fundamental group, which naturally leads to a “circular-orderability version” of the L-space conjecture. We also show that the fundamental groups of almost all graph manifolds are circularly orderable, and contrast the behaviour of circular-orderability and left-orderability with respect to the operations of Dehn surgery and taking cyclic branched covers.

Keywords

3-manifolds, graph manifolds, circularly orderable group, left-orderable group

Mathematical Subject Classification

Primary: 03C15, 06F15, 20F60, 57M50, 57M60

References

Publication

Received: 5 July 2022

Revised: 30 December 2023

Accepted: 12 February 2024

Published: 16 May 2025

Authors

Idrissa Ba
Department of Mathematics University of Manitoba Winnipeg, MB Canada

Adam Clay
Department of Mathematics University of Manitoba Winnipeg, MB Canada
https://adamjclay.github.io

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Volume 25, issue 2 (2025)