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

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HTLW02 - 3-manifold workshop

Co-author: Kimihiko Motegi (Nihon University)
 
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.   

This talk is part of the Isaac Newton Institute Seminar Series series.

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