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The crossings in a virtual 2-knot diagram are either
classical or virtual.
Classical crossing Classical crossing Virtual crossing
Crossings are closed curves or open intervals.
These disks cross in a circle. This tube crosses itself in an interval.
Forbidden triple points have forbidden moves in their movies.
unordered classical welded unwelded woven
2-knot diagrams are equivalent if related by Roseman moves.
I-bubble move
I-saddle move
II-bubble move
II-saddle move
Use the Roseman moves to separate the three spheres.
III-move
II-bubble moves
This works even if some of the crossings are virtual.