On the volume conjecture of the colored Jones invariants with arbitrary colors

Shinichiro Kakuta

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arXiv · 2604.10472

On the volume conjecture of the colored Jones invariants with arbitrary colors

Shinichiro Kakuta

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Abstract

We study the volume conjecture of the colored Jones invariants with sequences of colors corresponding to the deformation of the hyperbolic structure of a link complement. In particular, we investigate certain limits of the colored Jones invariants of the figure-eight knot and the Borromean rings and show that the limits are related to the volumes of hyperbolic cone manifolds whose singular sets are the links.

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Shinichiro Kakuta. 2026-04-12. On the volume conjecture of the colored Jones invariants with arbitrary colors. https://arxiv.org/abs/2604.10472

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