Linking invariants of even virtual links
Linking invariants of even virtual links
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DOI：
10.1142/s0218216517500729
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发表时间：
2017-10
影响因子：
0.5
通讯作者：
H. A. Miyazawa;K. Wada;A. Yasuhara
中科院分区：
文献类型：
--
作者：
H. A. Miyazawa;K. Wada;A. Yasuhara
如果虚拟交叉将每个组件分成偶数个弧，则虚拟链路图是偶数。偶虚链图集在经典和虚Reidemeister移动下是封闭的，它包含经典链图集。对于偶虚链接图，我们定义了一个类似于链接数的链接不变量。与通常的链接数不同，我们的链接不变量在禁止移动下不被保留。特别是，对于两个融合的同位素甚至虚拟链接图，它们的链接不变量之间的差异给出了一个下限的最小数量的禁止移动需要变形成其他。此外，我们给出了一个例子，表明下界是最好的可能。
A virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For an even virtual link diagram, we define a certain linking invariant which is similar to the linking number. In contrast to the usual linking number, our linking invariant is not preserved under the forbidden moves. In particular, for two fused isotopic even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.