On the volume conjecture for hyperbolic knots

2000/09/18 by Yoshiyuki Yokota, Yokota, Yoshiyuki · 5 citations
Mathematics · #57M25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0009165

10 pages, 6 figures

arxiv created 2000/09/18 · openalex publication_date 2000/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we give a rough, and so not complete yet, proof of Kashaev's conjecture, that is, the volume conjecture for hyperbolic knots, where the hyperbolicity equations associated to knot diagrams appear as the stationary phase equations for Kashaev's invariants.

Cited by

• On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume
• Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links
• Optimistic limits of colored Jones polynomials and complex volumes of hyperbolic links
• Quantum holonomic link invariants derived from stated skein algebras
• The colored Jones polynomial and the A-polynomial for twist knots

Related

• Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links
• The colored Jones polynomials and the simplicial volume of a knot
• An Introduction to the Volume Conjecture
• Approximations to the volume of hyperbolic knots
• Generalized Kashaev invariants for knots in three manifolds