论文标题
交替链接的灵巧性
Primeness of alternating virtual links
论文作者
论文摘要
使用称为Lassos的新工具，我们在封闭表面上的蜂窝链路{图表}与虚拟链接的等价类之间建立了一个新的对应关系。这类似于这些图表表示的链接之间的众所周知的对应关系，但具有至关重要的微妙之处。我们解释了在这些对应关系下，虚拟链接的传统概念比在增厚表面中的链接的链接更为严格。我们通过证明表面上的交替链路在更严格的意义上是典型的，除非它是``显然是'''复合材料。
Using a new tool called lassos, we establish a new correspondence between cellular link {diagrams} on closed surfaces and equivalence classes of virtual link {diagrams}. This is analogous to a well-known correspondence among the links represented by these diagrams, but with a crucial subtlety. We explain how, under these correspondences, the traditional notion of primeness for virtual links is stricter than the one for links in thickened surfaces. We extend a classical result of Menasco by proving that an alternating link in a thickened surface is prime in the stricter sense unless it is ``obviously" composite. (Adams et al and Howie--Purcell previously extended Menasco's result for the other notion of primeness.) We describe, given an alternating virtual link diagram, how to determine by inspection whether the virtual link it represents is prime in either sense.
