Mutants and SU(3)_q invariants
H. R. Morton, H. J. Ryder
TL;DR
This paper explores quantum knot invariants derived from SU(3)_q modules, demonstrating their ability to distinguish mutant knots and discussing skein-theoretic techniques for these invariants.
Contribution
It introduces specific SU(3)_q-module calculations that differentiate mutant knots and discusses Kuperberg's skein-theoretic methods in this context.
Findings
SU(3)_q invariants distinguish Conway and Kinoshita-Teresaka mutant knots
Details of quantum knot invariant calculations are provided
Discussion of skein-theoretic techniques for SU(3)_q invariants
Abstract
Details of quantum knot invariant calculations using a specific SU(3)_q-module are given which distinguish the Conway and Kinoshita-Teresaka pair of mutant knots. Features of Kuperberg's skein-theoretic techniques for SU(3)_q invariants in the context of mutant knots are also discussed.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · semigroups and automata theory