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

Presented by: 
Masakazu Teragaito Hiroshima University
Tuesday 31st January 2017 - 11:30 to 12:30
INI Seminar Room 1
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.   
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons