Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles.
Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles.
复制标题
没有显式 2-cocycle 的 qudle 2-cocycle 结不变量的计算。
DOI：
10.1142/s0218216517500353
复制
发表时间：
2017
影响因子：
0.5
通讯作者：
Saito,Masahico
中科院分区：
文献类型：
--
作者：
Clark,WEdwin;Dunning,LarryA;Saito,Masahico
我们探讨了一个结不变量来自相应的染色缠结与任意连接quandles。当quandle是某种类型的阿贝尔扩张时，该不变量等价于quandle上循环不变量。我们构造了许多这样的阿贝尔扩展使用广义亚历山大quandles没有明确发现上循环。这允许在不显示显式上循环的情况下构造多上循环不变量。我们证明了对于连通的广义亚历山大量子点，其不变量等价于Kubermann的结着色多项式.使用这种技术的计算表明，上循环不变量区分所有的定向素结多达11个交叉和最定向素结与12个交叉，包括分类对称性：镜像，反转，和反转镜。
We explore a knot invariant derived from colorings of corresponding-tangles with arbitrary connected quandles. When the quandle is an abelian extension of a certain type the invariant is equivalent to the quandle-cocycle invariant. We construct many such abelian extensions using generalized Alexander quandles without explicitly finding-cocycles. This permits the construction of many-cocycle invariants without exhibiting explicit-cocycles. We show that for connected generalized Alexander quandles the invariant is equivalent to Eisermann’s knot coloring polynomial. Computations using this technique show that the-cocycle invariant distinguishes all of the oriented prime knots up to 11 crossings and most oriented prime knots with 12 crossings including classification by symmetry: mirror images, reversals, and reversed mirrors.