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Generalized torsion orders and Alexander polynomials
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 08 January 2025, pp. 1-20
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Generalized Torsion Elements and Bi-orderability of 3-manifold Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 4 / 01 December 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 830-844
- Print publication:
- 01 December 2017
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- Article
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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.
