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Categorified Recurrence Relations and q-Holonomicity of Colored Knot Floer Homology

A construction of S^r-colored knot Floer homologies (built from Heegaard-Floer theory) that satisfy categorified recurrence relations - a homological lifting, via a Weyl-algebra notion of homological holonomicity, of the q-difference recurrences among polynomial knot invariants. Taking graded Euler characteristics recovers the q-holonomicity of the corresponding sequence of colored Alexander polynomials, in analogy with the AJ conjecture for colored Jones polynomials.

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HOLONOMICITY FROM A HEEGAARD-FLOER PERSPECTIVE BENJAMIN COOPER AND ROBERT DEYESO III Abstract. We

For a knot K and a simple Lie algebra, the Reshetikhin-Turaev construction yields a family of quantum invariants indexed by representations; q-holonomicity (the existence of a q-difference recurrence…