Creating subdivision rules from polyhedra with identifications

Details Creating subdivision rules from polyhedra with identifications Creating subdivision rules from polyhedra with identifications

2012-01-25

arxiv.org/abs/1201.5176v1

Mathematics

Geometric Topology

25 pages, 33 figures

Scientific paper

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 subdivision rule for many 3-manifolds from polyhedral gluings. The manifolds that satisfy the conditions include all closed manifolds created from right-angled hyperbolic polyhedra, as well as many 3-manifolds with toral or hyperbolic boundary.

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