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A new criterion for knots with free periods

Nafaa Chbili
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Abstract

Let $p\geq 2$ and $q\neq 0$ an integer. A knot $K$ in the three-sphere is said to be a $(p,q)$-lens knot if and only if it covers a link in the lens space $L(p,q)$. In this paper, we use the second coefficient of the HOMFLY polynomial to provide a necessary condition for a knot to be a $(p,q)$-lens knot. As an application, it is shown that this criterion rules out the possibility of being $(5,1)$-lens for 80 among the 84 knots with less than 9 crossings.

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Nafaa Chbili. 2003-10-29. A new criterion for knots with free periods. https://arxiv.org/abs/math/0310458

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