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

Kimihiko Motegi; Masakazu Teragaito

doi:10.4153/cmb-2017-008-8

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arXiv · 1608.08295

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

Kimihiko Motegi·Masakazu Teragaito

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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.

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BibTeX RIS

Kimihiko Motegi, Masakazu Teragaito. 2016-08-30. Generalized torsion elements and bi-orderability of 3-manifold groups. https://doi.org/10.4153/cmb-2017-008-8

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