Abstract
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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.
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Keywords
Chen–Yang conjecture, cone-manifold, potential function,
volume conjecture
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Mathematical Subject Classification
Primary: 57K14, 57K31, 57K32
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Milestones
Received: 11 July 2022
Revised: 18 December 2022
Accepted: 22 December 2022
Published: 3 May 2023
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