David De Wit, Louis H Kauffman, Jon R Links
Published 1998-11-23, updated 1998-11-24Version 2
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.
Comments: 35 pages, 20 figures. <ddw@maths.uq.edu.au>, <kauffman@uic.edu>, <http://math.uic.edu/~kauffman>, <jrl@maths.uq.edu.au>
Journal: Journal of Knot Theory and its Ramifications, 8(2):165-199, March 1999
The Links-Gould Invariant
The Kauffman Polynomials of 2-bridge Knots
On the Links-Gould invariant and the square of the Alexander polynomial
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