Conway spheres as ideal points of the character variety

TL;DR

This paper establishes a connection between Conway spheres in hyperbolic links and ideal points of the link's character variety, providing a new geometric interpretation of these spheres.

Contribution

It proves that Bonahon-Siebenmann Conway spheres correspond to ideal points of the link's character variety, linking geometric and algebraic perspectives.

Findings

Conway spheres are associated with ideal points of the character variety.

The result applies to hyperbolic links with Bonahon-Siebenmann families.

Provides a new geometric interpretation of Conway spheres.

Abstract

We prove that any Bonahon-Siebenmann family of Conway spheres for a hyperbolic link is associated to an ideal point of the character variety of the link.