...ng picture. + + + + + Two Gauss diagrams represent isotopic links if and only if they are related by a finite number of Reidemeister moves for Gauss diagrams shown in Figure 1, where ε = ±1. See e.g. =-=[2, 12, 13]-=-. Ω1 : ε Ω2 : ε −ε Ω3 : + + + + ++ Figure 1. Reidemeister moves of Gauss diagrams. 2.2. Gauss diagrams of closed braids. Recall that the Artin braid group Bm on m strings has the following presentatio...