Circular-orderability of 3-manifold groups

Ba, Idrissa¹ ; Clay, Adam¹

¹Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada

Algebraic and Geometric Topology, Tome 25 (2025) no. 2, pp. 791-825

Résumé

We initiate the study of circular-orderability of 3-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, ℙ2-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.

Détail

DOI : 10.2140/agt.2025.25.791

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

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