Dichromatic link invariants

Biased Graphs .III. Chromatic and Dichromatic Invariants

A Dichromatic Polynomial for Weighted Graphs and Link Polynomials

A dichromatic polynomial for weighted graphs is presented. The Kauffman bracket of a signed graph, an invariant inspired by the Jones polynomial of a link in three-space, is shown to be essentially an evaluation of this dichromatic polynomial, as are the homfly polynomials of certain particular types of links. 1. THE DICHROMATIC POLYNOMIAL OF A WEIGHTED GRAPH In this note we use the term graph ...

Vassiliev Homotopy String Link Invariants

We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular, Vassiliev invariants classify string links up to homotopy, and all Vassiliev homotopy string link invariants come from marked surfaces as in [3], using the same construction that in the case of knots gives...

New knot and link invariants

We study the new formulas of Th. Fiedler for the degree-3-Vassiliev invariants for knots in the 3-sphere and solid torus and present some results obtained by them. We show that a knot with Jones polynomial consisting of exactly two monomials must have at least 20 crossings.

Link invariants from finite racks

We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack’s second rack cohomology satisfying a new degeneracy conditio...