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arXiv · 1703.05911

Knot invariant with multiple skein relations

Zhiqing Yang
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Abstract

Given any oriented link diagram, one can construct knot invariants using skein relations. Usually such a skein relation contains three or four terms. In this paper, the author introduces several new ways to smooth a crossings, and uses a system of skein equations to construct link invariant. This invariant can also be modified by writhe to get a more powerful invariant. The modified invariant is a generalization of both the HOMFLYPT polynomial and the two-variable Kauffman polynomial. Using the diamond lemma, a simplified version of the modified invariant is given. It is easy to compute and is a generalization of the two-variable Kauffman polynomial.

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Zhiqing Yang. 2017-03-17. Knot invariant with multiple skein relations. https://arxiv.org/abs/1703.05911

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