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Modular $q$-holonomic modules

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arxiv 2203.17029 v1 pith:PZ7YHVBW submitted 2022-03-31 math.GT hep-thmath.CA

Stavros Garoufalidis , Campbell Wheeler This is my paper · ORCID
classification math.GThep-thmath.CA
keywords modularmodulesequationsholonomicchern--simonsdifferencelinearnotion
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abstract

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules of complex Chern--Simons theory are modular. This notion explains conceptually recent structural properties of quantum invariants of knots and 3-manifolds, and of exact and perturbative Chern--Simons theory, and in addition provides an effective method to solve the corresponding linear $q$-difference equations. An alternative title of our paper, emphasising the equations rather than the modules, is: Modular linear $q$-difference equations.

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Cited by 2 Pith papers

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

  1. On the Virasoro Crossing Kernels at Rational Central Charge

    hep-th 2025-12 conditional novelty 8.0 of 10

    At rational central charge, the Virasoro crossing kernels decompose into two admissible square-root-branched kernels; the physical c≤1 kernels are derived for the first time.

  2. Explicit classes in Habiro cohomology

    math.AG 2025-05 conditional novelty 7.0 of 10

    Explicit 'naive' Habiro cohomology classes are built from q-hypergeometric deformations and push-forwards, producing canonical q-deformations of Picard-Fuchs equations for Legendre, figure-eight A-polynomial, and quin...

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