论文标题
浓厚的圆环中的完全增强的链接
Fully Augmented Links in the Thickened Torus
论文作者
论文摘要
在本文中，我们研究了增厚的圆环中完全增强的链路补充的几何形状，并描述了它们的几何特性，从而概括了$ s^3 $的完全增强链接的研究。我们对增厚的圆环中的哪些完全增强的链路分类为双曲线，表明它们在增厚的圆环中的补充分解为理想的右角托尼德拉，并且这种分解的边缘是规范的。我们还研究了$ s^3 $的完全增强链接的量密度，定义为其体积和增强次数的比例。我们证明了完全增强链路的体积密度猜想，该链接指出，$ s^3 $中的一系列完全增强链路的体积密度在图中汇聚到双层链路，将其收敛到该双层链路的体积密度。
In this paper we study the geometry of fully augmented link complements in the thickened torus and describe their geometric properties, generalizing the study of fully augmented links in $S^3$. We classify which fully augmented links in the thickened torus are hyperbolic, show that their complements in the thickened torus decompose into ideal right-angled torihedra, and that the edges of this decomposition are canonical. We also study volume density of fully augmented links in $S^3$, defined to be the ratio of its volume and the number of augmentations. We prove the Volume Density Conjecture for fully augmented links which states that the volume density of a sequence of fully augmented links in $S^3$ which diagrammatically converge to a biperiodic link, converges to the volume density of that biperiodic link.
