#### Volume 12, issue 4 (2012)

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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