figure-eight knot

《Symplectic Geometry》 · 第 184 页 · Section 7.10，三股辫字的闭合构造

The group is generated by \(n-1\) elementary braids, each of which contains a single crossing. The generator \(\sigma_i\) is shown in Figure 7.13. Its inverse, \(\sigma_i^{-1}\), has a crossing of opposite sign. Writing down words in these braid generators provides a way to describe links without the use of pictures. For example \(\sigma_1\sigma_2^{-1}\sigma_1\sigma_2^{-1}\in B_3\) closes to give the figure-8 knot.