176 citations · 1.3k across the 156 of their papers we have counts for
5 papers · 2 filters
An Extended Bracket Polynomial for Virtual Knots and Links
Louis H. Kauffman
This paper defines a new invariant of virtual knots and links that we call the extended bracket polynomial, and denote by <<K>> for a virtual knot or link K. This invariant is a st…
Determinants of rational knots
Louis H. Kauffman, Pedro Lopes
We study the Fox coloring invariants of rational knots. We express the propagation of the colors down the twists of these knots and ultimately the determinant of them with the help…
A State Sum Link Invariant of Regular Isotopy
Louis H. Kauffman, Simon King, Sostenes Lins
This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial
Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces
Louis H. Kauffman, João Faria Martins
We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated wi…
Biquandles for Virtual Knots
David Hrencecin, Louis H. Kauffman
This paper studies an algebraic invariant of virtual knots called the biquandle. The biquandle generalizes the fundamental group and the quandle of virtual knots. The approach take…