标题： 复化四面体、基本群和双扭结的体积猜想 显示英文标题

标题： Complexified tetrahedrons, fundamental groups, and volume conjecture for double twist knots

摘要： 本文证明了双扭结的体积猜想。 主要工具是复化的四面体及其对应的 fundamental 群的 $\mathrm{SL}(2, \mathbb{C})$ 表示。 复化的四面体是一种截断或双重截断四面体的版本，其边长和二面角都被复化。 彩色琼斯多项式用量子 $6j$ 符号表示，该符号对应于复化的四面体。 显示英文摘要

摘要： In this paper, the volume conjecture for double twist knots are proved. The main tool is the complexified tetrahedron and the associated $\mathrm{SL}(2, \mathbb{C})$ representation of the fundamental group. A complexified tetrahedron is a version of a truncated or a doubly truncated tetrahedron whose edge lengths and the dihedral angles are complexified. The colored Jones polynomial is expressed in terms of the quantum $6j$ symbol, which corresponds to the complexified tetrahedron.