Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces
Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces
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利用最小亏格 Seifert 曲面的自由因子性质识别非伪交替结
DOI：
10.1142/s0218216521500723
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发表时间：
2021
影响因子：
0.5
通讯作者：
Masakazu Teragaito
中科院分区：
文献类型：
--
作者：
Keisuke Himeno;Masakazu Teragaito
通过其Seifert曲面，构造性地定义了伪交替节点和环。通过对原始平面进行Murasugi求和，得到这样的结点或链环作为结果曲面的边界。相反，很难确定给定的结点或链节是否为伪交替的。一个主要的困难是缺乏识别给定的Seifert曲面是否可分解为Murasugi和的标准。在本文中，我们提出了一种新的识别非伪交错纽结的方法。结合由缝合流形理论得到的极小亏格Seifert曲面的唯一性，我们证明了两类椒盐卷曲不是伪交错的。
Pseudo-alternating knots and links are defined constructively via their Seifert surfaces. By performing Murasugi sums of primitive flat surfaces, such a knot or link is obtained as the boundary of the resulting surface. Conversely, it is hard to determine whether a given knot or link is pseudo-alternating or not. A major difficulty is the lack of criteria to recognize whether a given Seifert surface is decomposable as a Murasugi sum.In this paper, we propose a new idea to identify non-pseudo-alternating knots. Combining with the uniqueness of minimal genus Seifert surface obtained through sutured manifold theory, we demonstrate that two infinite classes of pretzel knots are not pseudo-alternating.