The Jones polynomial of rational links
Khaled Qazaqzeh, Moh'd Yasein, and Majdoleen Abu-Qamar
TL;DR
This paper provides an explicit formula for computing the Jones polynomial of rational links using their continued fraction denominators, simplifying the process of analyzing these links.
Contribution
It introduces a novel explicit formula linking the Jones polynomial to the continued fraction representation of rational links.
Findings
Explicit formula for Jones polynomial of rational links
Simplifies computation of Jones polynomial for rational links
Connects continued fractions with knot invariants
Abstract
We give an explicit formula for the Jones polynomial of any rational link in terms of the denominators of the canonical continued fraction of the slope of the given rational link.
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