伴随扭曲Reidemeister挠与Gram矩阵
Adjoint twisted Reidemeister torsion and Gram matrices
AI总结：
本文计算了闭定向及带边双曲3-流形的伴随扭曲Reidemeister挠，基于Dehn填充和理想三角剖分给出了新公式，并在量子不变量的渐近展开研究中发挥重要作用。
摘要：
我们计算了闭定向双曲3-流形以及带环面边界的双曲3-流形的伴随扭曲Reidemeister挠。在我们的公式中，我们将流形视为沿基本阴影链环余补的合适边界分量进行Dehn填充而得到的，且该公式用边界分量经线的对数和乐表示。作为一个重要的特例，我们还写出了带全测地边界的双曲3-流形的加倍流形的伴随扭曲Reidemeister挠公式，该公式用流形的几何理想三角剖分的边长表示。这些出乎意料的公式受量子不变量的渐近展开研究\cite{WY}的启发，并在其中发挥了重要作用。
英文摘要：
We compute the adjoint twisted Reidemeister torsion for closed oriented hyperbolic $3$-manifolds and for hyperbolic $3$-manifolds with toroidal boundary. In our formula, we consider the manifold as obtained by doing a Dehn-filling along suitable boundary components of a fundamental shadow link complement, and the formula is in terms of the logarithmic holonomy of the meridians of the boundary components. As an important special case, we also write down a formula of the adjoint twisted Reidemeister torsion for the double of a hyperbolic $3$-manifold with totally geodesic boundary in terms of the edge lengths of a geometric ideal triangulation of the manifold. These unexpected formulas were inspired by, and played an important role in, the study of the asymptotic expansion of quantum invariants\,\cite{WY}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
