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On the potential function of the colored Jones polynomial with arbitrary colors

Shun Sawabe

Vol. 322 (2023), No. 1, 171–194
Abstract

We consider the potential function of the colored Jones polynomial for a link with arbitrary colors and obtain the cone-manifold structure for the link complement. In addition, we establish a relationship between a saddle point equation and hyperbolicity of the link complement. This provides evidence for the Chen–Yang conjecture on the link complement.

Keywords
Chen–Yang conjecture, cone-manifold, potential function, volume conjecture
Mathematical Subject Classification
Primary: 57K14, 57K31, 57K32
Milestones
Received: 11 July 2022
Revised: 18 December 2022
Accepted: 22 December 2022
Published: 3 May 2023
Authors
Shun Sawabe
Department of Pure and Applied Mathematics
School of Fundamental Science and Engineering
Waseda University
Tokyo
Japan

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