VARIATIONS IN WRITHES OF VIRTUAL KNOTS UNDER A LOCAL MOVE
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초록
n-writhes denoted by Jn(K) are virtual knot invariants for n 6= 0 and are closely associated with coecients of some polynomial invariants of virtual knots. In this work, we investigate the variations of Jn(K) under arc shift move and conclude that n-writhes Jn(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n 6= 0 we provide an in nite family of virtual knots which can be distinguished by n-writhes Jn(K), whereas odd writhe J(K) fails to do so.
Abstract
n-writhes denoted by Jn(K) are virtual knot invariants for n 6= 0 and are closely associated with coecients of some polynomial invariants of virtual knots. In this work, we investigate the variations of Jn(K) under arc shift move and conclude that n-writhes Jn(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n 6= 0 we provide an in nite family of virtual knots which can be distinguished by n-writhes Jn(K), whereas odd writhe J(K) fails to do so.
참고문헌 (14)
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