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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2007.1
- 수록면
- 329 - 334 (6page)
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By the works of Levine [2] and Rolfsen [5],[6], it is known that a local move called a crossing-change is strongly related to the Alexander invariant. In this note, we will consider to what degree the relationship is strong. Let K be a knot, and K× the set of knots obtained from a knot K by a singl crossing-change. Let MK be the Alexander invariant of a knot K, and MK the set of the Alexander invariants {MK}K2K for a set of knots K. Our main result is the following: If both K1 and K2 are knots with unknotting number one, then MK1 = MK2 implies MK×1 = MK×2 . On the other hand, there exists
a pair of knots K1 and K2 such that MK1 = MK2 and MK×1 6= MK×2 . In other words, the Gordian complex is not homogeneous with respect to Alexander invariant
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참고문헌 (7)
참고문헌 신청
/ 1937 / Die Gordische Aufl¨osung von Knoten : 680 ~ 696
/ 1965 / A characterization of knot polynomials 4 : 135 ~ 141
/ 1974 / A surgical view of Alexander’s polynomial, in Geometric Topology (Proc.Park City, 1974) 438 : 415 ~ 423
/ 1976 / Publish or Perish Inc.
/ 2002 / The Gordian complex of knots 11 : 363 ~ 368
/ 1965 / A characterization of knot polynomials 4 : 135 ~ 141
/ 1974 / A surgical view of Alexander’s polynomial, in Geometric Topology (Proc.Park City, 1974) 438 : 415 ~ 423
/ 1976 / Publish or Perish Inc.
/ 2002 / The Gordian complex of knots 11 : 363 ~ 368
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