On the Volume Conjecture for hyperbolic Dehn-filled $3$-manifolds along the figure-eight knot

Abstract

Using Ohtsuki's method, we prove the Asymptotic Expansion Conjecture and the Volume Conjecture of the Reshetikhin-Turaev and the Turev-Viro invariants for all hyperbolic $3$-manifolds obtained by doing a Dehn-surgery along the figure-$8$ knot.

arXiv comment57 pages, 6 figures

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Cited by in corpus (8)

• Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms II
• Discrete Fourier transforms, quantum $6j$-symbols and deeply truncated tetrahedra
• Fundamental shadow links realized as links in $S^3$
• A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds
• Asymptotics of some quantum invariants of the Whitehead chains
• Computation of leading coefficients in asymptotics of relative quantum invariants
• Volume conjecture, geometric decomposition and deformation of hyperbolic structures
• On the asymptotic expansion for the relative Reshetikhin-Turaev invariants of fundamental shadow link pairs