Equivalence of Cables Of Mutants of Knots
Equivalence of Cables Of Mutants of Knots
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结突变体电缆的等价性
DOI：
10.4153/cjm-1989-013-1
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
J. Przytycki
中科院分区：
文献类型：
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作者：
J. Przytycki
有一个很好的公式将链路的 (m, k)-电缆的亚历山大多项式与链路的亚历山大多项式联系起来 [5] [36] [38]。 H. Morton 和 H. Short 研究了类似的公式是否适用于 Jones-Conway (Homfly) 多项式，他们发现可能性很小。 Morton 和 Short 对沿结的 (2, q) 电缆的 Jones-Conway 多项式进行了许多计算（选择 2 是因为计算机的可能性有限），他们得到了非常有趣的实验材料 [24]、[25]。特别是，他们发现，使用他们的方法，他们能够从镜像中区分一些 Birman [4] 和 Lozano-Morton [22] 示例（他们尝试过的所有示例）和 942 结（采用 Rolfsen [37] 表示法）。另一方面，他们无法区分康威结和木下寺坂结。
There is the nice formula which links the Alexander polynomial of (m, k)-cable of a link with the Alexander polynomial of the link [5] [36] [38]. H. Morton and H. Short investigated whether a similar formula holds for the Jones-Conway (Homfly) polynomial and they found that it is very unlikely. Morton and Short made many calculations of the Jones-Conway polynomial of (2, q)-cables along knots (2 was chosen because of limited possibility of computers) and they get very interesting experimental material [24], [25]. In particular they found that using their method they were able to distinguish some Birman [4] and Lozano-Morton [22] examples (all which they tried) and the 942 knot (in the Rolfsen [37] notation) from its mirror image. On the other hand they were unable to distinguish the Conway knot and the Kinoshita-Terasaka knot.