The Links-Gould Invariant of Links
Geometric Topology
2009-09-25 v2 Quantum Algebra
Abstract
We introduce and study in detail an invariant of (1,1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra U_q[gl(2|1)], will be referred to as the Links-Gould invariant. We find that our invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (detecting chirality of some links where these invariants fail), and that it does not distinguish mutants or inverses. The method of evaluation is based on an abstract tensor state model for the invariant that is quite useful for computation as well as theoretical exploration.
Keywords
Cite
@article{arxiv.math/9811128,
title = {The Links-Gould Invariant of Links},
author = {David De Wit and Louis H Kauffman and Jon R Links},
journal= {arXiv preprint arXiv:math/9811128},
year = {2009}
}
Comments
35 pages, 20 figures. <[email protected]>, <[email protected]>, <http://math.uic.edu/~kauffman>, <[email protected]>