A proof of the Teichmüller TQFT volume conjecture for 7₃ knot

2023/07/24 by Uemura, Soichiro
#57M25 #57M27 #57M50 #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2307.12848

Abstract

In the generalized topological quantum field theory constructed by Andersen and Kashaev, invariants of 3-manifolds are defined given the combinatorial structure of a tetrahedral decomposition. Furthermore, a variant of the volume conjecture has been proposed in which the hyperbolic volume can be extracted from this invariant of the complementary space of the hyperbolic knot in an oriented 3-dimensional closed manifold. We prove that the reformulated volume conjecture holds for the complementary space of the hyperbolic knot 7₃ in S³, given a specific tetrahedral decomposition.

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• Asymptotic aspects of the Teichmüller TQFT
• The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
• An Introduction to the Volume Conjecture
• On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the figure-eight knot