论文标题
Turaev-Viro不变性和布线操作
Turaev-Viro invariants and cabling operations
论文作者
论文摘要
在本文中，我们研究了Turaev-viro不变性的变化，以$ 3 $ - manifolds，带有环形边界，在附加$（P，Q）$ - 有线空间的操作下。我们将结果应用于陈和阳的猜想，该猜想将Turaev-Viro不变性的渐近性与紧凑型$ 3 $ MANIFOLD的简单体积联系起来。对于$ p $和$ q $ coprime，我们表明chen-yang量猜想在$ \ left（p，q \ right）$ - 电缆下稳定。我们通过研究Reshetikhin--turaev $ so_3 $ -Topological量子场理论（TQFT）的线性操作员$ rt_r $与Torus结电缆空间相关的线性$ rt_r $，在其中TQFT是众所周知的，与所需的Turaev-viro invariants密切相关。特别是，我们利用的方法依赖于我们提供必要和充分条件的线性操作员的可逆性。
In this paper, we study the variation of the Turaev--Viro invariants for $3$-manifolds with toroidal boundary under the operation of attaching a $(p,q)$-cable space. We apply our results to a conjecture of Chen and Yang which relates the asymptotics of the Turaev--Viro invariants to the simplicial volume of a compact oriented $3$-manifold. For $p$ and $q$ coprime, we show that the Chen--Yang volume conjecture is stable under $\left(p,q\right)$-cabling. We achieve our results by studying the linear operator $RT_r$ associated to the torus knot cable spaces by the Reshetikhin--Turaev $SO_3$-Topological Quantum Field Theory (TQFT), where the TQFT is well-known to be closely related to the desired Turaev--Viro invariants. In particular, our utilized method relies on the invertibility of the linear operator for which we provide necessary and sufficient conditions.
