论文标题
考夫曼支架互换和音量猜想
Kauffman bracket intertwiners and the volume conjecture
论文作者
论文摘要
体积猜想将量子不变性和双曲线几何形状相关联。 Bonahon-Wong-Yang通过使用两个同构不可替代表示，引入了一个新版本的音量猜想。互换者是由表面差异性建造的。当差异性是伪anosov时，他们制定了体积的猜想。在本文中，我们使用从封闭的圆环的绞线代数到量子圆环的代数嵌入封闭式圆环的所有互换器，并显示与这些互助仪的痕迹相关的极限。此外，我们考虑具有负欧拉特征的表面的周期性差异性，并且猜想相应的极限为零，因为周期性差异性的映射Tori的简单体积为零。对于曾经刺穿的圆环，我们对互换者进行精确的计算，并证明我们的猜想。
The volume conjecture relates the quantum invariant and the hyperbolic geometry. Bonahon-Wong-Yang introduced a new version of the volume conjecture by using the intertwiners between two isomorphic irreducible representations of the skein algebra. The intertwiners are built from surface diffeomorphisms; they formulated the volume conjecture when diffeomorphisms are pseudo-Anosov. In this paper, we explicitly calculate all the intertwiners for the closed torus using an algebraic embedding from the skein algebra of the closed torus to a quantum torus, and show the limit superior related to the trace of these intertwiners is zero. Moreover, we consider the periodic diffeomorphisms for surfaces with negative Euler characteristic, and conjecture the corresponding limit is zero because the simplicial volume of the mapping tori for periodic diffeomorphisms is zero. For the once punctured torus, we make precise calculations for intertwiners and prove our conjecture.
