On a Conjecture by Kauffman on Alternative and Pseudoalternating Links
On a Conjecture by Kauffman on Alternative and Pseudoalternating Links
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考夫曼关于替代和伪交替链接的猜想
DOI：
10.1016/j.topol.2015.03.012
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Marithania Silvero
中科院分区：
文献类型：
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作者：
Marithania Silvero
众所周知，交替链接是伪交替的。1983年，路易斯·考夫曼（Louis Kauffman）推测，这两个阶级是相同的。本文证明了对于第一贝蒂数不大于2的链路，Kauffman猜想成立。然而，当这个值增加时，它通常是不正确的，因为我们也通过找到两个反例来证明：一个连杆和一个结，它们的第一个贝蒂数分别等于3和4。我们研究的是由彼得·克伦威尔提出的同质链的中间家族。
It is known that alternative links are pseudoalternating. In 1983 Louis Kauffman conjectured that both classes are identical. In this paper we prove that Kauffman Conjecture holds for those links whose first Betti number is at most 2. However, it is not true in general when this value increases, as we also prove by finding two counterexamples: a link and a knot whose first Betti numbers equal 3 and 4, respectively. In the way we work with the intermediate family of homogeneous links, introduced by Peter Cromwell.