Seifert circle

《Symplectic Geometry》 · 第 103 页 · Section 5.1，平滑与 Seifert circles 的命名

If the link is unoriented then choose an orientation for each component. Choose a diagram for the link in the \(xy\)-plane in \(\mathbb R^3\). In a small neighbourhood of each crossing, make the following local change to the diagram: delete the crossing and reconnect the loose ends in the only way compatible with the orientation. […] When this has been done at every crossing, the diagram becomes a set of disjoint simple loops in the plane — it is a diagram with no crossings. These loops are called Seifert circles.

《Mathematical Physics: Classical Mechanics》 · 第 16 页 · Chapter 2，Seifert circuits 的同义命名

Let \(D\) be an oriented diagram for the oriented link \(L\) and let \(\widehat D\) be \(D\) modified as shown in Figure 2.2. \(\widehat D\) is the same as \(D\) except in a small neighbourhood of each crossing where the crossing has been removed in the only way compatible with the orientation. […] In the above proof, \(\widehat D\) was a collection of disjoint simple closed curves constructed from \(D\). These curves are called the Seifert circuits of \(D\).