Generalized torsion elements and bi-orderability of 3-manifold groups

Abstract

It is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of 3-manifolds, and verify the conjecture for non-hyperbolic, geometric 3-manifolds. We also confirm the conjecture for some infinite families of closed hyperbolic 3-manifolds. In the course of the proof, we prove that each standard generator of the Fibonacci group F(2,m) (m>2) is a generalized torsion element.

14 pages, no figure

References in corpus (3)

• Residual nilpotence and ordering in one-relator groups and knot groups
• Generalized torsion in knot groups
• Testing bi-orderability of knot groups

Cited by in corpus (4)

• Generalized torsion elements in groups
• Generalized torsion elements in infinite groups
• Generalized torsion orders of generalized torsion elements
• Circular orderability of 3-manifold groups