2014/09/08 by Brian Rushton, Rushton, Brian
Computer Science · Engineering · Mathematics · #05C25 #20F65 #52C22 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:05C25 #msc:20F65 #msc:52C22
paper · pdf · doi:10.48550/arxiv.1409.2563
To appear in Conformal Geometry and Dynamics, published by the American Mathematical Society
openalex publication_date 2014/09/08 · arxiv created 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperbolic group determines the Gromov boundary. We give a criterion for a subdivision rule to represent a Euclidean space of dimension less than 4. We also show that Nil and Sol geometries can not be modeled by subdivision rules. We use these tools and previous theorems to classify the geometry of subdivision rules for low-dimensional geometric groups by the combinatorial properties of their subdivision rules.