2006/05/23 by Louis H. Kauffman, Kauffman, Louis H. · 1 citation
Mathematics · #57M27 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0605622
LaTeX document, 35 pages, 21 figures
arxiv created 2006/05/23 · arxiv updated 2009/12/01
This paper is an introduction to the state sum model for the Alexander-Conway polynomial that was introduced in the the author's book "Formal Knot Theory" (Princeton University Press, 1983). The article outlines how Alexander's original definition of the polynomial as the determinant of a matrix associated with the link diagram can be reformulated as a state summation over combinatorial configurations of the diagram. Facts about the state model, the Clock Theorem (that makes this model tick) and relations with other state models such as the bracket polynomial, are discussed. The paper includes a miniature introduction to Khovanov homology. This paper will appear in the forthcoming Dover republication of Formal Knot Theory.