2025/12/29 by Ka Ho Wong, Wong, Ka Ho
Mathematics · #57K31 #57K32 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2512.23198
openalex publication_date 2025/12/29 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28
We introduce a generalized FAMED property for ideal triangulations of hyperbolic knot complements in \mathbbS3. Given a hyperbolic knot K in \mathbbS3 and a semi-geometric triangulation X of \mathbbS3 ∖ K that is generalized FAMED with respect to the longitude. We prove that in the semi-classical limit ℏ → 0+, for any angle structure α, the partition function \mathscrZ_ℏ(X,α) in Teichmüller TQFT decays exponentially with decrease rate the volume of \mathbbS3 ∖ K equipped with a hyperbolic cone structure determined by α, and that the 1-loop invariant of Dimofte-Garoufalidis emerges as the 1-loop term. With additional combinatorial conditions on the triangulations, we prove the existence of the Jones function and show that its decay rate is governed by the Neumann-Zagier potential function. In particular, the Andersen-Kashaev volume conjecture holds for every hyperbolic knot whose complement admits such kinds of triangulations.