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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.9
- 수록면
- 511 - 518 (8page)
- DOI
- 10.5666/KMJ.2024.64.3.511
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초록· 키워드
오류제보하기
A 2n-move is a local change for knots and links which changes 2n-half twists to 0-half twists or vice versa for a natural number n. In 1979, Yasutaka Nakanishi conjectured that the 4-move is an unknotting operation. This is still an open problem. It is known that the Γ-polynomial is an invariant for oriented links which is the common zeroth coefficient polynomial of the HOMFLYPT and Kauffman polynomials. In this paper, we show that the 4k-move is not an unknotting operation for any integer k(≥ 2) by using the Γ-polynomial, and if Γ(K; -1) ≡ 9 (mod 16) then the knot K cannot be deformed into the unknot by a single 4-move. Moreover, we give a one-to-one correspondence between the value Γ(K; -1)(mod 16) and the pair (a2(K), a4(K)) (mod 2) of the second and fourth coefficients of the Alexander-Conway polynomial for a knot K.
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