Generalized Torsion Elements and Bi-orderability of 3-manifold Groups
2017 ◽
Vol 60
(4)
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pp. 830-844
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AbstractIt 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.
2020 ◽
Vol 29
(11)
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pp. 2050079
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2013 ◽
Vol 50
(1)
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pp. 31-50
Keyword(s):
2019 ◽
Vol 52
(5)
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pp. 1305-1329
Keyword(s):
2019 ◽
Vol 2019
(753)
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pp. 23-56
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Keyword(s):
2011 ◽
Vol 54
(1)
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pp. 33-45
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