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The Forbidden Number of a Knot

Blake Mellor|Alissa S. Crans|Sandy Ganzell
경북대학교 자연과학대학 수학과|2015.06|Kyungpook Mathematical Journal|제55권 제2호|pp. 485-506

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키워드

virtual knotforbidden moveodd writhe
주제분류수학

초록

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 forbid-den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

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 forbid-den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

참고문헌 (22)

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