CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
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 generalized torsion element, bi-ordering, 3-manifold group
MSC Classifications: 57M25, 57M05, 06F15, 20F05 show english descriptions Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Fundamental group, presentations, free differential calculus
Ordered groups [See also 20F60]
Generators, relations, and presentations
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
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/