2005/12/04 by Louis H. Kauffman, Kauffman, Louis H., R. Bruce Richter +1
Computer Science · Engineering · Mathematics · #57M27 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Interconnection Networks and Systems #Polynomial and algebraic computation #math.GT #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0512091
11 pages, LaTeX document, 4 figures
openalex publication_date 2005/12/04 · arxiv created 2005/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper gives a polynomial invariant for flat virtual links. In the case of one component, the polynomial specializes to Turaev's virtual string polynomial. We show that Turaev's polynomial has the property that it is non-zero precisely when there is no filamentation of the knot, as described by Hrencecin and Kauffman. Schellhorn has provided a version of filamentations for flat virtual links. Our polynomial has the property that if there is a filamentation, then the polynomial is 0. The converse fails, although if the polynomial is 0, then it turns out to be easy to determine if there is a filamentation.