论文标题
$ n $ - 空间图
$N$-quandles of spatial graphs
论文作者
论文摘要
基本问题是打结，链接和空间图的强大不变，但是通常很难确定两个问题是否是同构。一种方法是查看Quandle的商，例如Joyce \ Cite {Jo}定义的$ n $ Quandle;特别是，Hoste和Shanahan \ cite {HS2}将结与有限的$ n $ Quandles分类。 Mellor和Smith \ Cite {MS}引入了链接的$ n $ Quandle，作为对乔伊斯的$ n $ quandle的概括，并提出了与有限的$ n $ Quandles的链接分类。我们将$ n $ Quandle推广到空间图，并研究哪些空间图具有有限的$ n $ Quandles。我们证明了关于空间图的$ n $ Quandles的基本结果，并猜想了具有有限$ n $ Quandles的空间图的分类，从而扩展了\ cite {MS}中链接的猜想。我们在几种情况下验证了猜想，还提出了一个可能的反例。
The fundamental quandle is a powerful invariant of knots, links and spatial graphs, but it is often difficult to determine whether two quandles are isomorphic. One approach is to look at quotients of the quandle, such as the $n$-quandle defined by Joyce \cite{JO}; in particular, Hoste and Shanahan \cite{HS2} classified the knots and links with finite $n$-quandles. Mellor and Smith \cite{MS} introduced the $N$-quandle of a link as a generalization of Joyce's $n$-quandle, and proposed a classification of the links with finite $N$-quandles. We generalize the $N$-quandle to spatial graphs, and investigate which spatial graphs have finite $N$-quandles. We prove basic results about $N$-quandles for spatial graphs, and conjecture a classification of spatial graphs with finite $N$-quandles, extending the conjecture for links in \cite{MS}. We verify the conjecture in several cases, and also present a possible counterexample.
