Circular orderability of 3-manifold groups

Abstract

This paper initiates the study of circular orderability of $3$-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, ${\mathbb{P}}^2$-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 circularly orderability and left-orderability with respect to the operations of Dehn surgery and taking cyclic branched covers.

35 pages, 2 figures. This version has minor changes to the mathematical content, and substantial changes to the exposition. To appear in Algebraic and Geometric Topology (AGT)

References in corpus (2)

• Free products of circularly-ordered groups with amalgamated subgroup
• Circularly ordering direct products and the obstruction to left-orderability