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Large color $R$-matrix for knot complements and strange identities

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arxiv 2004.02087 v2 pith:ISSYCJZR submitted 2020-04-05 math.GT hep-thmath-phmath.MPmath.QA

Sunghyuk Park This is my paper
classification math.GThep-thmath-phmath.MPmath.QA
keywords knotsbraidcolorcomplementsidentitiesknotlargelinks
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abstract

The Gukov-Manolescu series, denoted by $F_K$, is a conjectural invariant of knot complements that, in a sense, analytically continues the colored Jones polynomials. In this paper we use the large color $R$-matrix to study $F_K$ for some simple links. Specifically, we give a definition of $F_K$ for positive braid knots, and compute $F_K$ for various knots and links. As a corollary, we present a class of `strange identities' for positive braid knots.

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Cited by 3 Pith papers

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

  1. Resurgence of Chern-Simons theory at the trivial flat connection

    math.GT 2021-11 unverdicted novelty 8.0 of 10

    An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory a...

  2. 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.

  3. 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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