论文标题
广义扭转元素和双曲线链接
Generalized torsion elements and hyperbolic links
论文作者
论文摘要
在一个组中，广义扭转元素是一个非身份元素，其偶联物的某些非空产品产生了身份。这样的元素是一个可以双订单的障碍物。我们表明，几周的歧管，人物八姐妹歧管以及怀特黑德姐妹链接的补充允许其基本群体中广泛的扭转元素。特别是，Whitehead Sister Link是类型（-2,3,8）的椒盐脆饼链接，可以推广到类型（-2,3,2n）的双曲线椒盐脆饼链接，n> 3。这些给出了双曲线链接的第一个示例，其链接组允许广义扭转元素。
In a group, a generalized torsion element is a non-identity element whose some non-empty finite product of its conjugates yields the identity. Such an element is an obstruction for a group to be bi-orderable. We show that the Weeks manifold, the figure-eight sister manifold, and the complement of Whitehead sister link admit generalized torsion elements in their fundamental groups. In particular, the Whitehead sister link, which is the pretzel link of type (-2,3,8), can be generalized to hyperbolic pretzel links of type (-2,3,2n), n>3. These give the first examples of hyperbolic links whose link groups admit generalized torsion elements.
