Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial

Abstract

We discuss multivariable invariants of colored links associated with the $N$-dimensional root of unity representation of the quantum group. The invariants for $N>2$ are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When $(N,3)=1$ and $N$ is odd, the invariant does not vanish for the parallel link (cable) of the knot $3_1$, while the Alexander polynomial vanishes for the cable link.

19 pages

References in corpus (2)

• Cyclic monodromy matrices for sl(n) trigonometric R-matrices
• Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

Cited by in corpus (3)

• The colored Jones polynomials and the simplicial volume of a knot
• Multivariable link invariants arising from Lie superalgebras of type I
• Automatic Evaluation of the Links-Gould Invariant for all Prime Knots of up to 10 Crossings