论文标题
浸入扁平丝带结
Immersed flat ribbon knots
论文作者
论文摘要
我们研究了浸泡的平面色带结和链接的最小色带长度。我们的方法是将这种结的空间嵌入，并将其链接到更大的磁盘图中更大的空间。当磁盘图空间中的长度最小符为色带时，这些解决了功能区的问题。当磁盘图空间中的最小化器不是色带并说明一些猜想时，我们还提供了示例。我们计算一些小结和链路图的最小色调以及某些无限的链接图家族。最后，我们为在所有图中的结中呈现了一个结节或链接的最小色带长度的交叉数。
We study the minimum ribbonlength for immersed planar ribbon knots and links. Our approach is to embed the space of such knots and links into a larger more tractable space of disk diagrams. When length minimisers in disk diagram space are ribbon, then these solve the ribbonlength problem. We also provide examples when minimisers in the space of disk diagrams are not ribbon and state some conjectures. We compute the minimal ribbonlength of some small knot and link diagrams and certain infinite families of link diagrams. Finally we present a bound for the number of crossings for a diagram yielding the minimum ribbonlength of a knot or link amongst all diagrams.
