A kernel of braid group representation yields a knot with trivial knot polynomials
A kernel of braid group representation yields a knot with trivial knot polynomials
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辫子组表示的核心产生具有平凡结多项式的结
DOI：
10.1007/s00209-015-1426-7
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发表时间：
2015
影响因子：
0.8
通讯作者：
Tetsuya Ito
中科院分区：
文献类型：
--
作者：
Aleksic;et al.;齋藤隆之;T. Saito;T. Saito;T. Saito;齋藤隆之;齋藤隆之;齋藤隆之;齋藤隆之;Tetsuya Ito and Keiko Kawamuro;Tetsuya Ito and Keiko Kawamuro;Tetsuya Ito
我们证明了辫子群的非平凡非中心正规子群包含一个辫子，该辫子的闭包是一个具有任意大亏格的双曲纽结。这表明量子表示的不忠实性意味着相应的量子不变量无法检测到解结。证明利用了辫子群的Dehornoy排序。
We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that the non-faithfulness of a quantum representation implies that the corresponding quantum invariant fails to detect the unknot. The proof utilizes the Dehornoy ordering of the braid groups.