论文标题
交替链接的经典结果
Classical results for alternating virtual links
论文作者
论文摘要
我们将Bankwitz，Crowell和Murasugi的一些经典结果扩展到虚拟链接的设置。例如，我们表明，当且仅当它被明显拆分时，交替的虚拟链接才会拆分，并且任何几乎经典的虚拟链接的亚历山大多项式都在交替。第一个结果是与任何非分类交替链接的链接决定因素和交叉数相关的不平等的结果。第二个是Bott和Mayberry的矩阵树定理的结果。我们将第一个结果扩展到半定虚拟链接。我们讨论了虚拟和焊接链接的Tait猜想，并注意Tait的第二个猜想对于交替的焊接链接不是正确的。
We extend some classical results of Bankwitz, Crowell, and Murasugi to the setting of virtual links. For instance, we show that an alternating virtual link is split if and only if it is visibly split, and that the Alexander polynomial of any almost classical alternating virtual link is alternating. The first result is a consequence of an inequality relating the link determinant and crossing number for any non-split alternating virtual link. The second is a consequence of the matrix-tree theorem of Bott and Mayberry. We extend the first result to semi-alternating virtual links. We discuss the Tait conjectures for virtual and welded links and note that Tait's second conjecture is not true for alternating welded links.
