location:  Publications → journals → CMB
Abstract view

# Generalized Torsion Elements and Bi-orderability of 3-manifold Groups

Published:2017-03-08
Printed: Dec 2017
• Kimihiko Motegi,
Department of Mathematics, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156--8550, Japan
• Masakazu Teragaito,
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima 739--8524, Japan.
 Format: LaTeX MathJax PDF

## 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 $F(2, m)$ ($m \gt 2$) is a generalized torsion element.
 Keywords: generalized torsion element, bi-ordering, 3-manifold group
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M05 - Fundamental group, presentations, free differential calculus 06F15 - Ordered groups [See also 20F60] 20F05 - Generators, relations, and presentations

 top of page | contact us | privacy | site map |