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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Constructing subdivision rules from polyhedra with identifications

Brian Rushton

Algebraic & Geometric Topology 12 (2012) 1961–1992
Abstract

Cannon, Swenson and others have proved numerous theorems about subdivision rules associated to hyperbolic groups with a 2–sphere at infinity. However, few explicit examples are known. We construct an explicit finite subdivision rule for many 3–manifolds obtained from polyhedral gluings. The manifolds that satisfy the conditions include all manifolds created from compact right angled hyperbolic polyhedra, as well as many 3–manifolds with toral or hyperbolic boundary.

Keywords
finite subdivision rule, hyperbolic polyhedra
Mathematical Subject Classification 2010
Primary: 20F67, 57M50
References
Publication
Received: 24 January 2012
Revised: 5 June 2012
Accepted: 9 July 2012
Published: 27 October 2012
Authors
Brian Rushton
Department of Mathematics
Temple University
Room 638 Wachman Hall
1805 N. Broad Street
Philadelphia, PA 19122
USA
https://sites.google.com/site/rushtonresearch/home