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 quintic families.
Modular $q$-holonomic modules
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Explicit classes in Habiro cohomology
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 quintic families.