2009/08/11 by Micah Chrisman, Chrisman, Micah W.
Computer Science · Mathematics · #57M25 #57M27 #Complexity and Algorithms in Graphs #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0908.1538
openalex publication_date 2009/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≤ n if and only if an invariant is a polynomial of degree ≤ 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.