Knot complement, ADO invariants and their deformations for torus knots. (English) Zbl 1459.57017
Summary: A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of \(\text{ADO}_3\) polynomial of torus knots is provided.
MSC:
| 57K14 | Knot polynomials |
| 57K16 | Finite-type and quantum invariants, topological quantum field theories (TQFT) |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Keywords:
torus knots; knot complement; quantum invariant; \(q\)-series; ADO polynomials; Chern-Simons theory; categorificationReferences:
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