Homogeneity of dynamically defined wild knots

Wild Knots as limit sets of Kleinian Groups

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $Λ$ also fibers over the circle. As a consequence, the universal covering of $\mathbb{S}^{3}-Λ$ is $\mathbb{R}^{3}$. We prove that the complement of a dynamically-defined fibered wild knot can not be a complete hyperbolic 3-manifold.

A wild knot $\mathbb{S}^{2}\hookrightarrow\mathbb{S}^{4}$ as limit set of a Kleinian Group: Indra's pearls in four dimensions

The purpose of this paper is to construct an example of a 2-knot wildly embedded in $\mathbb{S}^{4}$ as the limit set of a Kleinian group. We find that this type of wild 2-knots has very interesting topological properties.

用镶嵌图驯服野结

Taming Wild Knots with Mosaics

本文提出用镶嵌图理论研究具有孤立野点的野结子类，引入镶嵌结团和镶嵌刚性顶点空间图概念，拓展了传统结分类方法。

$N$维串珠项链与受 Schottky 群不变的高维野结

$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group

本文基于$n$维结和串珠项链，利用共形Schottky群构造了具有Cantor集野点的高维野结，证明其纤维化性质，并研究了循环分支覆盖，推广了已有结果。

嵌入梅尔森海绵中的野结

Wild knots embedded in the Menger Sponge

本文通过递归构造了无数非等价的嵌入梅尔森海绵中的野结，并能控制其在通常康托尔集中的野点集。还展示了由克莱因群作用动态定义的野结可被同胚到海绵中。

野生纽结的一个非分类结果

A Non-classification Result for Wild Knots

该研究运用描述集合论方法，证明了野生纽结分类问题的难度严格高于可数结构的分类问题，给出了相关非分类结果。