The Forbidden Number of a Knot

  • Received : 2014.06.16
  • Accepted : 2014.10.07
  • Published : 2015.06.23


Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.


virtual knot;forbidden move;odd writhe


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