论文标题
基本的影子链接在$ s^3 $中实现为链接
Fundamental shadow links realized as links in $S^3$
论文作者
论文摘要
我们使用纯粹的拓扑工具在3个球体中构建了几个无限的双曲线连接家族，使Chen and Yang构成的Turaev-Viro不变体积构想。为了证明我们的链接满足了量的猜想，我们证明每个链接都具有同质形态的补充，与基本的阴影链接的补充相辅相成。这些是$ s^2 \ times s^1 $的连接副本中的链接，因为贝莱蒂，detcherry，detcherry，kalfagianni和Yang为此而闻名。我们的方法还验证了几个双曲线链接的猜想，其交叉数小于十二。此外，我们表明$ 3 $ -SPHERE中的每个链接都是满足猜想的链接的斜系链接。作为我们结果的应用，我们扩展了满足AMU猜想的已知示例类别，这些示例对表面映射类组的量子表示。例如，我们在$ g $表面的映射类组中提供了明确的元素，其中包含任何$ g $的四个边界组件。为此，我们使用Detcherry和Kalfagianni开发的技术，将Turaev-Viro不变体积猜想与AMU猜想相关联。
We use purely topological tools to construct several infinite families of hyperbolic links in the 3-sphere that satisfy the Turaev-Viro invariant volume conjecture posed by Chen and Yang. To show that our links satisfy the volume conjecture, we prove that each has complement homeomorphic to the complement of a fundamental shadow link. These are links in connected sums of copies of $S^2 \times S^1$ for which the conjecture is known due to Belletti, Detcherry, Kalfagianni, and Yang. Our methods also verify the conjecture for several hyperbolic links with crossing number less than twelve. In addition, we show that every link in the $3$-sphere is a sublink of a link that satisfies the conjecture. As an application of our results, we extend the class of known examples that satisfy the AMU conjecture on quantum representations of surface mapping class groups. For example, we give explicit elements in the mapping class group of a genus $g$ surface with four boundary components for any $g$. For this, we use techniques developed by Detcherry and Kalfagianni which relate the Turaev-Viro invariant volume conjecture to the AMU conjecture.
