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.
From 3-dimensional skein theory to functions near Q
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abstract
Motivated by the Quantum Modularity Conjecture and its arithmetic aspects related to the Habiro ring of a number field, we define a map from the Kauffman bracket skein module of an integer homology 3-sphere to the Habiro ring, and use Witten's conjecture (now a theorem) to show that the image is an effectively computable module of finite rank that can be used to phrase the quantum modularity conjecture.
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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.