Figures & data
Fig. 1 On the left is the trefoil knot drawn using the Gauss code O1U2O3U1O2U3, as you can see by starting at the indicated point and following the knot along, writing down the crossings in the order you encounter them and whether you cross over or under until you return to the starting point. On the right we draw a knot diagram with the Gauss code O1U2U1O2. One must then introduce an extra “virtual crossing” to join the end back up to the starting point.
Fig. 2 Allowing both forbidden moves, Funder or Fover , would render the theory of virtual knots trivial, since every two virtual knot diagrams are equivalent by a sequence of virtual and forbidden moves.
