2013/07/06 by Brian Rushton, Rushton, Brian
Computer Science · Mathematics · #20F36 #57N16 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F36 #msc:57N16
paper · pdf · doi:10.48550/arxiv.1307.1788
32 pages, 33 figures. Significantly expanded to include subdivision rules for all special cubulated groups. Includes several applications of subdivision rules related to quasi-isometries
openalex publication_date 2013/07/06 · arxiv created 2013/10/28 · arxiv updated 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect properties such as growth, ends, divergence, etc. We include figures of several worked out examples.