The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic sequences

Details The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic sequences The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic sequences

2010-11-29

arxiv.org/abs/1011.6329v3

Mathematics

Geometric Topology

10 pages, 3 figures, 2 Mathematica notebooks

Scientific paper

The SL_3 colored Jones polynomial of the trefoil knot is a $q$-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for the annihilator ideal of this $q$-holonomic sequence as a case study. On the one hand, our results are new and useful to quantum topology: this is the first example of a rank 2 Lie algebra computation concerning the colored Jones polynomial of a knot. On the other hand, this work illustrates the applicability and computational power of the employed computer algebra methods.

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