论文标题
Turaev-Viro不变式的相对版本和双曲线三个manifolds的体积
A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds
论文作者
论文摘要
我们定义了Turaev-Viro不变性的相对版本，用于理想的三角形紧凑型3个序列，具有非空边界和边缘上的颜色，从而推广了歧管的Turaev-Viro不变性[35]。我们还提出了这些不变式的体积猜想，它们的渐近行为与双曲双曲线度量公制中的歧管体积有关[22，23]，而奇异基因座是由颜色确定的边缘和锥角，并证明了锥形角度足够小的猜想。这表明了解决Chen-Yang [8]提出的Turaev-Viro不变式的体积猜想的方法，该方法对具有完全测量边界的双曲线3个manifolds提出。
We define a relative version of the Turaev-Viro invariants for an ideally triangulated compact 3-manifold with non-empty boundary and a coloring on the edges, generalizing the Turaev-Viro invariants [35] of the manifold. We also propose the Volume Conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold in the hyperbolic polyhedral metric [22, 23] with singular locus the edges and cone angles determined by the coloring, and prove the conjecture in the case that the cone angles are sufficiently small. This suggests an approach of solving the Volume Conjecture for the Turaev-Viro invariants proposed by Chen-Yang [8] for hyperbolic 3-manifolds with totally geodesic boundary.
