A new two-variable generalization of the Jones polynomial

Dimos Goundaroulis; Sofia Lambropoulou

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arXiv · 1608.01812

A new two-variable generalization of the Jones polynomial

Dimos Goundaroulis·Sofia Lambropoulou

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Abstract

We present a new 2-variable generalization of the Jones polynomial that can be defined through the skein relation of the Jones polynomial. The well-definedness of this new generalization is proved both algebraically and diagrammatically as well as via a closed combinatorial formula. This new invariant is able to distinguish more pairs of non-isotopic links than the original Jones polynomial such as the Thistlethwaite link from the unlink with two components.

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Dimos Goundaroulis, Sofia Lambropoulou. 2016-08-05. A new two-variable generalization of the Jones polynomial. https://arxiv.org/abs/1608.01812

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