Asymptotics of quantum invariants of surface diffeomorphisms II: The figure-eight knot complement

Francis Bonahon; Helen Wong; Tian Yang

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arXiv · 2203.05730

Asymptotics of quantum invariants of surface diffeomorphisms II: The figure-eight knot complement

Francis Bonahon·Helen Wong·Tian Yang

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Abstract

In earlier work, the authors introduced a conjecture which, for an orientation-preserving diffeomorphism $\varphi \colon S \to S$ of a surface, connects a certain quantum invariant of $\varphi$ with the hyperbolic volume of its mapping torus $M_\varphi$. This article provides a proof of this conjecture in the simplest case where it applies, namely when the surface $S$ is the one-puncture torus and the mapping torus $M_\varphi$ is the complement of the figure-eight knot.

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BibTeX RIS

Francis Bonahon, Helen Wong, Tian Yang. 2022-03-11. Asymptotics of quantum invariants of surface diffeomorphisms II: The figure-eight knot complement. https://arxiv.org/abs/2203.05730

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