Where the Links--Gould invariant first fails to distinguish nonmutant prime knots
Where the Links--Gould invariant first fails to distinguish nonmutant prime knots
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链接所在——古尔德不变量首先无法区分非突变素数结
DOI：
10.1142/s0218216507005658
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发表时间：
2005
影响因子：
0.5
通讯作者：
J. Links
中科院分区：
文献类型：
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作者：
D. D. Wit;J. Links
众所周知，第一个双变量Links-Gould量子链路不变量LG≡LG2,1比HOMFLYPT和Kauffman多项式更强大，因为它区分了最多10个交叉点的所有素数结（包括反射）。在这里，我们报告了极大地扩展了素数节的LG的评价集的调查。通过它们，我们证明了对于多达11个交点的所有素数结（包括反射）不变量是完全模突变的，但不能区分一些12个交点的素数结的非突变对。作为副产品，我们将突变体分类在11和12个交叉点的素数结内。同时，我们了解到LG区分了最多12个交叉的所有手性素数结的手性。然后，我们证明了每个突变不敏感链不变量都不能区分一些14交素数节的手性。这提供了14个交联的手性素数结的例子，其手性是LG无法区分的。
It is known that the first two-variable Links–Gould quantum link invariant LG ≡ LG2,1 is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations of LG for prime knots. Through them, we show that the invariant is complete, modulo mutation, for all prime knots (including reflections) of up to 11 crossings, but fails to distinguish some nonmutant pairs of 12-crossing prime knots. As a byproduct, we classify the mutants within the prime knots of 11 and 12 crossings. In parallel, we learn that LG distinguishes the chirality of all chiral prime knots of at most 12 crossings. We then demonstrate that every mutation-insensitive link invariant fails to distinguish the chirality of a number of 14-crossing prime knots. This provides 14-crossing examples of chiral prime knots whose chirality is undistinguished by LG.
LG多项式和考夫曼多项式之间的关系
DOI：
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发表时间：
--
期刊：
Topology and its Applications (in press)
影响因子：
--
作者：
N.Nakamura;et al.;N.Nakamura;石井 敦
通讯作者：
石井 敦
LG 多项式是 Alexander-Conway 多项式的推广
DOI：
--
发表时间：
--
期刊：
Pacific Journal of Mathematics (in press)
影响因子：
--
作者：
N.Nakamura;et al.;N.Nakamura;石井 敦;石井 敦
通讯作者：
石井 敦