FIGURE 1. Classical and Virtual crossings
FIGURE 2. Generalized Reidemeister moves
FIGURE 3. Detour move
FIGURE 4. Local writhe or sign of a crossing
FIGURE 5. Gauss diagram corresponding to virtual figure eight knot
FIGURE 6. Reidemeister moves on Gauss diagram
FIGURE 7. Forbidden moves Fu and Fo
FIGURE 8. Arc (a,b) and (e,f)
FIGURE 9. Equivalent Arcs (a,b) and (c,d)
FIGURE 10. Arc shift on arc (a,b)
FIGURE 11. Equivalent diagrams corresponding to arc shift on arc (a,b)
FIGURE 12. Arc shift reverses orientation of arc (a,b) in D(a,b)
FIGURE 13. Arc shift move on arc (a,b)
FIGURE 14. Gauss diagram analogues to the arc shift moves shown in Fig. 13.
FIGURE 15
FIGURE 16. Arc shift move twice on same arc results in equivalent diagram
FIGURE 17. sign(c') = - sign(c)
FIGURE 18. R3 move realized via arc shift moves
FIGURE 19
FIGURE 20. ∆-move realized using arc shift moves
FIGURE 21. Turning a Gauss diagram into parallel chord diagram
FIGURE 22. Unknotting virtual trefoil using arc shift move
FIGURE 23
FIGURE 24. Region arc shift on region R1 and R2
FIGURE 25. Realizing forbidden move Fu using region arc shift
FIGURE 26. Region arc shift number is 1 for both knots
FIGURE 27
FIGURE 28. Forbidden detour move
FIGURE 29. FD move via region arc shift at region R
References
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