Symplectic Geometry
《Symplectic Geometry》 · 第 215–216 页 · Section 9.1，Andrei Markov 的辫字变换列表（原页的共轭符号为等价关系）
In §7.10 and Exercise 7.12.18 we introduced the \(n\)-string braid group \(B_n\). […] Andrei Markov proposed the following set of moves: the analogous Reidemeister moves are indicated in parentheses. Braid relations: \(\sigma_i\sigma_j=\sigma_j\sigma_i\) when \(|i-j|\ge2\) (isotopy in the plane), \(\sigma_i\sigma_i^{-1}=1=\sigma_i^{-1}\sigma_i\) (Reidemeister 2), \(\sigma_i\sigma_{i+1}\sigma_i=\sigma_{i+1}\sigma_i\sigma_{i+1}\) (Reidemeister 3). Conjugacy: \(\sigma_i\beta\sigma_i^{-1}\equiv\beta\equiv\sigma_i^{-1}\beta\sigma_i\). Stabilisation: replace \(\beta\in B_n\) with \(\beta\sigma_n^{\pm1}\in B_{n+1}\) or vice versa (Reidemeister 1).