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Knot Complement, ADO-Invariants and their Deformations for Torus Knots

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arxiv 2007.13277 v3 pith:NZSAS2U2 submitted 2020-07-27 math.GT hep-thmath-phmath.MPmath.QA

John Chae This is my paper
classification math.GThep-thmath-phmath.MPmath.QA
keywords invariantknotknotstorusado-invariantscomplementseriesakutus-deguchi-ohtsuki
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A relation between the two-variable series knot invariant and the Akutus-Deguchi-Ohtsuki(ADO)-invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for certain ADO-invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of ADO_3-polynomial of torus knots is provided.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A supergroup series for knot complements

    math.GT 2025-08 unverdicted novelty 7.0 of 10

    Defines the three-variable superalgebra series F_K(y,z,q) for knot complements, derives its surgery relation to hat Z(q), and computes examples for torus knots.

  2. Quantum invariants of 3-manifolds and links: a review

    math-ph 2025-09 unverdicted novelty 1.0 of 10

    This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.

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