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.
Perturbative invariants of cusped hyperbolic 3-manifolds
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abstract
We prove that a formal power series associated to an ideally triangulated cusped hyperbolic 3-manifold (together with some further choices) is a topological invariant. This formal power series is conjectured to agree to all orders in perturbation theory with two important topological invariants of hyperbolic knots, namely the Kashaev invariant and the Andersen--Kashaev invariant (also known as the state-integral) of Teichm\"uller TQFT.
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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.