论文标题
在划分缎带打结的表面的结上
On knots that divide ribbon knotted surfaces
论文作者
论文摘要
如果它是色带2结的横截面，我们将结的定义为半色带，并观察到色带意味着半色带意味着切片。我们介绍了结k的半色属，这是k是横截面的带状表面的最小属。我们计算了所有素数的属，最多可达12个十字架，并为许多13个横断打结。相同的方法产生了双层属属的新计算。我们还介绍了一个打结K的半融合数，该融合数衡量了k是横截面的带2节的复杂性。我们表明，它是由Levine-Tristram签名从下面界定的，并且与标准融合数不同。
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of which K is a cross-section. We compute this genus for all prime knots up to 12 crossings, and many 13-crossing knots. The same approach yields new computations of the doubly slice genus. We also introduce the half fusion number of a knot K, that measures the complexity of ribbon 2-knots of which K is a cross-section. We show that it is bounded from below by the Levine-Tristram signatures, and differs from the standard fusion number by an arbitrarily large amount.
