Generalized Torsion Elements and Bi-orderability of 3-manifold Groups
Generalized Torsion Elements and Bi-orderability of 3-manifold Groups
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DOI：
10.4153/cmb-2017-008-8
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发表时间：
2016-08
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影响因子：
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通讯作者：
Kimihiko Motegi;M. Teragaito
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文献类型：
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作者：
Kimihiko Motegi;M. Teragaito
已知二阶群没有广义扭元，但广义扭元的匡威一般不成立。我们猜想，逆3-流形的基本群成立，并验证了非双曲，几何3-流形的猜想。我们还证实了一些闭双曲三维流形无穷族的猜想。在证明过程中，我们证明了Fibonacci群$F（2，m）\，（m>2）$的每个标准生成元都是广义挠元。
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 $F(2,m)\,(m>2)$ is a generalized torsion element.