论文标题
带有非平凡的订单中心的分支扭转旋转的表示
Representations of branched twist spins with a non-trivial center of order 2
论文作者
论文摘要
众所周知，通过添加对应于圆圈动作的常规轨道和特定关系器的发电机，从原始1结组的连线呈现中获得了分支扭转旋转的结组的呈现。特别是，附加发电机是结组中心的元素。在本文中，我们专注于$ {\ rm sl} _2（\ mathbb {z} _3）$ - 表示和二面体组表示。对于前一种情况，我们为存在$ {\ rm sl} _2（\ mathbb {z} _3）$ - 表示分支扭曲旋转的表示形式提供了足够的条件。对于后一种情况，我们确定分支扭曲旋转的均衡二面体组表示的数量。
It is known that a presentation of the knot group of a branched twist spin is obtained from a Wirtinger presentation of the original 1-knot group by adding a generator corresponding to a regular orbit of the circle action and a certain relator. In particular, the additional generator is an element of the center of the knot group. In this paper, we focus on ${\rm SL}_2(\mathbb{Z}_3)$-representations and dihedral group representations. For the former case, we give a sufficient condition for the existence of an ${\rm SL}_2(\mathbb{Z}_3)$-representation for a branched twist spin. For the latter case, we determine the number of even-ordered dihedral group representations of branched twist spins.
