Wild knots in higher dimensions as limit sets of Kleinian groups

TL;DR

This paper constructs infinitely many wild knots in dimensions 2 to 5 as limit sets of geometrically finite Kleinian groups, expanding understanding of their geometric and topological properties.

Contribution

It introduces new examples of wild knots in higher dimensions as limit sets of Kleinian groups, a novel connection in geometric topology.

Findings

Existence of infinitely many wild knots in dimensions 2 to 5.

Each wild knot is realized as a limit set of a geometrically finite Kleinian group.

Some properties of these wild knots are described.

Abstract

In this paper we construct infinitely many wild knots, $\mathbb{S}^{n}\hookrightarrow\mathbb{S}^{n+2}$, for $n=2,3,4$ and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties