Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Forbidden Number of a Knot

  • CRANS, ALISSA S. (Department of Mathematics, Loyola Marymount University) ;
  • MELLOR, BLAKE (Department of Mathematics, Loyola Marymount University) ;
  • GANZELL, SANDY (Department of Mathematics and Computer Science, St. Mary's College of Maryland)
  • Received : 2014.06.16
  • Accepted : 2014.10.07
  • Published : 2015.06.23
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Abstract

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.

Keywords

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