On a Conjecture by Kauffman on Alternative and Pseudoalternating Links

Marithania Silvero

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arXiv · 1402.4599

On a Conjecture by Kauffman on Alternative and Pseudoalternating Links

Marithania Silvero

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Abstract

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.

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Marithania Silvero. 2014-02-19. On a Conjecture by Kauffman on Alternative and Pseudoalternating Links. https://arxiv.org/abs/1402.4599

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