A subtle new invariant for framed knots and links
Lins, Sostenes
Original · EN
We produce a facial state sum on plane diagrams of a knot or a link which admits an invariant specialization under Polyak's recent set of generating of 4 Reidemeister moves. Thus an isotopy invariant of framed links is obtained. Each state is a complete coloring of the faces of the diagram into white and black faces so that no two black faces share an edge. Each state induces a monomial in a ring of 16 variables. The sum of the states, properly specialized defines the new invariant. In despite of its simplicity it complements Jones invariant in distinguishing mirror pairs of links. In particular it proves that 9₄₂ is distinct from its mirror image. For this pair of knots both the Jones Polynomial and Kauffman 2-variable polynomial fail.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.