The Kauffman Polynomial of Periodic Links
Khaled Qazaqzeh, Ayman Aboufattoum, and Kyle Istvan
TL;DR
This paper establishes a congruence relation for a specialization of the Kauffman polynomial in periodic links, providing a new criterion to determine link periodicity based on polynomial invariants.
Contribution
It introduces a novel congruence relating the Kauffman polynomial of periodic links to their mirror images, offering a simple test for link periodicity.
Findings
Derived a congruence relation for the Kauffman polynomial of periodic links.
Provided a new criterion for detecting link periodicity.
Enhanced understanding of polynomial invariants in knot theory.
Abstract
We give a congruence relating a one variable specialization of the two variable Kauffman polynomial of any periodic link to that of its mirror image. Consequently, we obtain a new and simple criterion for periodicity of links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Graph theory and applications · Advanced Combinatorial Mathematics