Mathematics – Geometric Topology
Scientific paper
2000-04-27
Journal of Knot Theory and its Ramifications 12(6):(September 2003) 739-749
Mathematics
Geometric Topology
11 pages, 2 tables, 1 figure. Jon R Links: <jrl@maths.uq.edu.au>, David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw/>
Scientific paper
In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U_q[gl(2|1)]. We have implemented Mathematica code to evaluate the invariants for all prime knots up to 10 crossings.
Links Jon R.
Wit David de
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