论文标题
Vortex重新连接的拓扑
Topology of Vortex Reconnection
论文作者
论文摘要
打结的涡流，例如克莱克纳（Kleckner）和尔湾（Irvine）在水中产生的涡流，倾向于通过重新连接到无结织和未链接圆圈的收集来转变。链接$ k $的定向结的重新连接号$ r（k）$是解开/UNLINK $ K $所需的重新连接（定向重新平滑）的最小数量。将这个问题置于结的背景下，我们使用拉斯穆森的不变式表明，正结的重新连接数量等于其Seifert跨越表面的两倍。尤其是$（a，b）$ torus not具有$ r =（a-1）（b-1）。$ $ $ $ n link $ k $，$ r（k）= c（k）-s（k）-s（k） + 1 $，其中$ c（k）$是$ k $ and $ k $ and $ s（k）$的交叉数量，是$ k $ s（k）$的ciffect ciffers ciffers的数量，是cigrest ciff的数量。
Knotted vortices such as those produced in water by Kleckner and Irvine tend to transform by reconnection to collections of unknotted and unlinked circles. The reconnection number $R(K)$ of an oriented knot of link $K$ is the least number of reconnections (oriented re-smoothings) needed to unknot/unlink $K$. Putting this problem into the context of knot cobordism, we show, using Rasmussen's Invariant that the reconnection number of a positive knot is equal to twice the genus of its Seifert spanning surface. In particular an $(a,b)$ torus knot has $R = (a-1)(b-1).$ For an arbitrary unsplittable positive knot or link $K$, $R(K) = c(K) - s(K) + 1$ where $c(K)$ is the number of crossings of $K$ and $s(K)$ is the number of Seifert circles of $K.$ Examples of vortex dynamics are illustrated in the paper.
