发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究尖点三维流形的KLV配分函数，证明其渐近性由双曲锥结构的体积和挠率决定，并引入Reshetikhin--Turaev型函数，将归一化KLV配分函数表示为该函数平方范数的加权积分，推广了Turaev--Viro与Reshetikhin--Turaev不变量之间的关系。
AI 中文摘要
我们研究了Kashaev--Luo--Vartanov（KLV）配分函数的渐近性质和TQFT型性质。我们证明，该配分函数仅通过其外围角全纯依赖于规定的角结构。对于实现双曲锥结构的尖点三维流形的任何几何三角剖分，我们将配分函数的指数衰减率和1环项分别表示为相应双曲锥结构的体积和伴随扭曲Reidemeister挠率。因此，这些渐近公式对任何具有与几何角结构相同的外围角全纯的角结构均成立。我们进一步引入了一个与某些可容许的Neumann--Zagier数据相关联的Reshetikhin--Turaev型函数，扩展了Ben Aribi和作者先前研究的Teichmüller TQFT中的Jones函数。我们证明，在组合归一化之后，对于任何三角剖分，KLV配分函数可以表示为Reshetikhin--Turaev型函数的平方范数的加权积分，其中权重由外围曲线的角全纯决定。特别地，对于FAMED三角剖分，Reshetikhin--Turaev型函数与Jones函数一致，因此归一化的KLV配分函数通过对定义Teichmüller TQFT配分函数的被积函数的平方范数进行积分而获得。这提供了Turaev--Viro与Reshetikhin--Turaev不变量之间关系的非紧致类比。
英文摘要
We study the asymptotic and TQFT-type properties of the Kashaev--Luo--Vartanov (KLV) partition function. We show that the partition function depends on the prescribed angle structure only through its peripheral angular holonomies. For any geometric triangulation of a cusped 3-manifold realizing a hyperbolic cone structure, we express the exponential decay rate and the 1-loop term of the partition function in terms of, respectively, the volume and the adjoint twisted Reidemeister torsion of the corresponding hyperbolic cone structure. Consequently, these asymptotic formulas hold for any angle structure having the same peripheral angular holonomies as the geometric one. We further introduce a Reshetikhin--Turaev-type function associated with certain admissible Neumann--Zagier data, extending the Jones function in Teichmüller TQFT previously studied by Ben Aribi and the author. We show that, after a combinatorial normalization, for any triangulation, the KLV partition function can be expressed as a weighted integral of the squared norm of the Reshetikhin--Turaev-type function, where the weight is determined by the angular holonomies of peripheral curves. In particular, for FAMED triangulations, the Reshetikhin--Turaev-type function agrees with the Jones function, so that the normalized KLV partition function is obtained by integrating the squared norm of the integrand defining the Teichmüller TQFT partition function. This provides a noncompact analogue of the relationship between Turaev--Viro and Reshetikhin--Turaev invariants.
Comments38 pages, 3 figures
