Constructing subdivision rules from alternating links
Brian C. Rushton
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.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques