# Constructing subdivision rules from alternating links

## TL;DR

This paper constructs subdivision tilings for the complements of all nonsingular, prime alternating links, creating a combinatorial space at infinity that parallels hyperbolic group structures.

## Contribution

It introduces a method to generate subdivision tilings for alternating link complements, linking geometric group theory with link theory.

## Key findings

- Subdivision tilings are constructed for all nonsingular, prime alternating links.
- The tilings define a combinatorial space at infinity analogous to hyperbolic groups.
- Provides new examples connecting link complements with hyperbolic structures.

## Abstract

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link. These tilings define a combinatorial space at infinity, similar to the space at infinity for word hyperbolic groups.