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arXiv · 0908.1538

Twist Lattices and the Jones-Kauffman Polynomial for Long Virtual Knots

Micah W. Chrisman
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Abstract

In this paper, we investigate twist sequences for Kauffman finite-type invariants and Goussarov-Polyak-Viro finite-type invariants. It is shown that one obtains a Kauffman or GPV type of degree $\le n$ if and only if an invariant is a polynomial of degree $\le n$ on every twist lattice of the right form. The main result of this paper is an application of this technique to the coefficients of the Jones-Kauffman polynomial. It is shown that the Kauffman finite-type invariants obtained from these coefficients are not GPV finite-type invariants of any degree by explicitly showing they can never be polynomials. This generalizes a result of Kauffman, where it is known for degree $k=2$.

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BibTeXRIS

Micah W. Chrisman. 2009-08-11. Twist Lattices and the Jones-Kauffman Polynomial for Long Virtual Knots. https://arxiv.org/abs/0908.1538

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