A new arcade-based planarization technique plus the Kuperberg bracket yields a closed system of classical relations toward su3 A-polynomials, demonstrated on the trefoil.
Skein recursion for holomorphic curves and invariants of the unknot
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abstract
We determine the skein-valued Gromov-Witten partition function for a single toric Lagrangian brane in $\mathbb{C}^3$ or the resolved conifold. We first show geometrically they must satisfy a certain skein-theoretic recursion, and then solve this equation. The recursion is a skein-valued quantization of the equation of the mirror curve. The solution is the expected hook-content formula.
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On geometric bases for A-polynomials II: $\mathfrak{su}_3$ and Kuberberg bracket
A new arcade-based planarization technique plus the Kuperberg bracket yields a closed system of classical relations toward su3 A-polynomials, demonstrated on the trefoil.