A Habiro ring of a number field is constructed, with K3-graded modules, and perturbative quantum invariants are shown to be elements of these modules.
Algebraic aspects of holomorphic quantum modular forms
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abstract
Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the $(-2,3,7)$-pretzel knot.
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The Habiro ring of a number field
A Habiro ring of a number field is constructed, with K3-graded modules, and perturbative quantum invariants are shown to be elements of these modules.