The quantum A-polynomial conjecture for the knot series
The quantum A-polynomial conjecture for the knot series
Let be a knot, let be its rescaled knot series, let be the quantum polynomial of , and let be its Alexander polynomial. Define the symmetric expansion of a rational function in as the average of its Laurent expansion at and its Laurent expansion in at . Quantum A-polynomial conjecture. The quantum polynomial annihilates the knot series,
and its classical limit is the symmetric expansion of the reciprocal Alexander polynomial,
This conjecture links the quantum polynomial recursion to the Alexander polynomial and is presented as a refinement motivated by the AJ conjecture; the source supplies no resolution status.
Sources & referencesView supporting material
Primary source
Miranda C. N. Cheng, Francesca Ferrari and Gabriele Sgroi, “Three-Manifold Quantum Invariants and Mock Theta Functions”, arXiv:1912.07997 (2020).
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