198710.fig.0016
Figure 16: Deformation of strings and two reconnection moves, plus an exchange of two ends of strings and a rotation of one of the ends of the string, change the configuration (a) back to itself. Note that from (a) to (b) we exchange the two ends of strings, and from (d) to (e) we rotate one of the ends of the string by 360°. The combination of those moves does not generate any phase.