mutation

《Symplectic Geometry》 · 第 177–178、180 页 · Section 7.8，Definition 7.8.1 的输入与完整 Definition 7.8.4；三个主轴由第 180 页前段指定

A marked 2-tangle is a round ball \(B\) that contains two disjoint properly embedded arcs, and a (possibly empty) set of disjoint embedded loops. The four ends of the arcs meet the boundary sphere in points that are equally spaced around a great circle (called the equator); we label them in sequence around the circle with NW, NE, SE and SW, and view them so that they appear as in Figure 7.6. The arcs and loops are oriented: each arc is directed from an input to an output, and we choose NW and SE to be inputs and NE and SW to be outputs. […] A rotation of 180° about an axis perpendicular to the equatorial plane leaves the tangles \(t_0\) and \(t_\infty\) unchanged. Similarly, rotations of 180° about the vertical North-South axis or the horizontal East-West axis, followed by reversing the orientation of the strings, are also symmetry operations. […] Let \(L_1\) be an oriented link which contains a marked tangle \(t\). Remove \(t\), rotate it by 180° about one of its three principal axes, reversing all orientations if necessary, and glue it back in position to form a new link \(L_2\). If \(t\) itself has some symmetry then \(L_1\) and \(L_2\) may be the same. If \(L_1\) and \(L_2\) are different they are called mutants of each other.