On composite knots with symmetric union presentations
On composite knots with symmetric union presentations
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关于具有对称联合表示的复合结
DOI：
10.1142/s0218216519500652
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发表时间：
2019
影响因子：
0.5
通讯作者：
田中利史
中科院分区：
文献类型：
--
作者：
Tanaka;Toshifumi;Toshifumi Tanaka;田中利史
在三维空间中，一个纽结和它的镜像（它关于一个2-平面是对称的），通过将它们与一些垂直的有扭曲的2-弦缠结和一个水平的没有沿着扭曲的2-弦缠结连接起来，得到一个对称并集。本文引入了对称并的最小扭数，证明了如果一个纽结是一个具有最小扭数1的复合对称并，则有一个非平凡纽结及其镜像作为连通和项.作为应用，我们研究了对称并的最小扭数，证明了存在无穷多个最小扭数为2的对称并。
A symmetric union in the 3-spaceis obtained from a knot inand its mirror image, which is symmetric with respect to a 2-plane in, by connecting them with some vertical 2-string tangles with twists and a horizontal 2-string tangle with no twists along the plane. We introduce the minimal twisting number of a symmetric union and show that if a knotis a composite symmetric union with minimal twisting number one, thenhas a non-trivial knot and its mirror image as connected summands. As an application, we study the minimal twisting number of a symmetric union and show that there exist infinitely many symmetric unions with minimal twisting number two.