braid

《Symplectic Geometry》 · 第 183–184 页 · Section 7.10，Cylindrical tangles 中 n-string braid 及等价关系的定义

A cylindrical \(n\)-tangle is a ball \(D^2\times[0,1]\) with a line of \(n\) inputs in the top (\(D^2\times1\)) and a line of \(n\) outputs directly below them at the bottom. […] Each disc \(D^2\times x\) in the cylinder meets the inhabitant in exactly \(n\) points, once in each string; there are no extra loops. Such a tangle is called an \(n\)-string braid. Its strings descend monotonically without reversing anywhere. Braids are equivalent if they are isotopic using braid-preserving isotopies so that all the intervening positions are also braids.