Fundamental biquandles of ribbon 2-knots and ribbon torus-knots with isomorphic fundamental quandles
Fundamental biquandles of ribbon 2-knots and ribbon torus-knots with isomorphic fundamental quandles
复制标题
带状 2 结和带状环面结的基本双分形与同构基本分形
DOI：
10.1142/s0218216514500011
复制
发表时间：
2014
影响因子：
0.5
通讯作者：
Sosuke Ashihara
中科院分区：
文献类型：
--
作者：
Ryosuke Saito;Kunio Kaiho;Masahiro Oba;Satoshi Takahashi ,Zong-Qiang Chen;Li Tian;Jing Chen and Jinnan Tong;日野原由未;角田健太郎;Sosuke Ashihara
基本二分形和双分形是经典结和表面结的不变量。目前尚不清楚是否存在具有同构基本分位数和不同基本双分位数的经典结或表面结。我们证明具有同构基本四分位数的带状 2 结或带状环面结具有同构基本双分位数。为此，我们给出了一种从带状 2 结/环面结的基本二分形中获得其基本双分形的表示的方法。
The fundamental quandles and biquandles are invariants of classical knots and surface knots. It is unknown whether there exist classical or surface knots which have isomorphic fundamental quandles and distinct fundamental biquandles. We show that ribbon 2-knots or ribbon torus-knots with isomorphic fundamental quandles have isomorphic fundamental biquandles. For this purpose, we give a method for obtaining a presentation of the fundamental biquandle of a ribbon 2-knot/torus-knot from its fundamental quandle.