Kyungpook Mathematical Journal 2015; 55(2): 485-506
Published online June 23, 2015
Copyright © Kyungpook Mathematical Journal.
The Forbidden Number of a Knot
Alissa S. Crans1, Blake Mellor1 and Sandy Ganzell2
1Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, California 90045, USA
2Department of Mathematics and Computer Science, St.~Mary's College of Maryland, St.~Mary's City, MD 20686, USA
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 {it forbidden number}. We relate the forbidden number to several known invariants, and calculate bounds for some classes of
virtual knots.
Keywords: virtual knot, forbidden move, odd writhe