• Publications
  • Influence
Virtual Knot Theory
  • L. Kauffman
  • Computer Science, Mathematics
    Eur. J. Comb.
  • 5 November 1998
This paper is an introduction to the theory of virtual knots. It is dedicated to the memory of Francois Jaeger.
State Models and the Jones Polynomial
IN THIS PAPER I construct a state model for the (original) Jones polynomial [5]. (In [6] a state model was constructed for the Conway polynomial.) As we shall see, this model for the Jones polynomial
Knots And Physics
Physical Knots States and the Bracket Polynomial The Jones Polynominal and Its Generalizations Braids and Polynomials: Formal Feynman Diagrams, Bracket as Vacuum-Vacmum expectation and the Quantum
An invariant of regular isotopy
This paper studies a two-variable Laurent polynomial invariant of regular isotopy for classical unoriented knots and links. This invariant is denoted LK for a link K, and it satisfies the axioms: 1.
An Introduction to Knot Theory
This paper concentrates on the construction of invariants of knots, such as the Jones polynomials and the Vassiliev invariants, and the relationships of these invariants to other mathematics (such as
Formal Knot Theory
New invariants in the theory of knots
Approche diagrammatique des invariants dans la theorie des nœuds. Relations avec la theorie des graphes, la physique et d'autres sujets. Construction du polynome de Jones et de son algebre associee.
Invariants of graphs in three-space
Par association d'une collection de nœuds et d'aretes a un graphe dans un espace tridimensionnel, on obtient des invariants calculables du type de plongement du graphe. On considere deux types
A Tutte polynomial for signed graphs
  • L. Kauffman
  • Computer Science, Mathematics
    Discret. Appl. Math.
  • 1 September 1989
A generalization of the Tutte polynomial that is defined for signed graphs to provide a link between knot theory and graph theory, and to explore a context embracing both subjects.
Signature of links
Let L be an oriented tame link in the three sphere S3. We study the Murasugi signature, a(L), and the nullity, r(L). It is shown that a(L) is a locally flat topological concordance invariant and that