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

Kimihiko Motegi, Masakazu Teragaito

Published 2016-08-30Version 1

It is well 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 an infinite family of closed hyperbolic $3$--manifolds.