A Cantor set with hyperbolic complement

TL;DR

This paper constructs a specific Cantor set in three-dimensional space whose complement can be endowed with a complete hyperbolic metric, linking fractal geometry with hyperbolic 3-manifold theory.

Contribution

It introduces a novel example of a Cantor set in S^3 with a hyperbolic complement, bridging fractal and hyperbolic geometry.

Findings

The complement of the constructed Cantor set admits a complete hyperbolic metric.

The construction provides a new example connecting Cantor sets and hyperbolic 3-manifolds.

The result expands understanding of the geometric structures possible in fractal complements.

Abstract

We construct a Cantor set in S^3 whose complement admits a complete hyperbolic metric.