Perturbative invariants of cusped hyperbolic 3-manifolds

Stavros Garoufalidis; Matthias Storzer; Campbell Wheeler

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arXiv · 2305.14884

Perturbative invariants of cusped hyperbolic 3-manifolds

Stavros Garoufalidis·Matthias Storzer·Campbell Wheeler

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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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Stavros Garoufalidis, Matthias Storzer, Campbell Wheeler. 2023-05-24. Perturbative invariants of cusped hyperbolic 3-manifolds. https://arxiv.org/abs/2305.14884

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