Geometriae Dedicata

, Volume 167, Issue 1, pp 23–34 | Cite as

A finite subdivision rule for the n-dimensional torus

Original paper


Cannon, Floyd, and Parry have studied subdivisions of the 2-sphere extensively, especially those corresponding to 3-manifolds, in an attempt to prove Cannon’s conjecture. There has been a recent interest in generalizing some of their tools, such as extremal length, to higher dimensions. We define finite subdivision rules of dimension n, and find an n − 1-dimensional finite subdivision rule for the n-dimensional torus, using a well-known simplicial decomposition of the hypercube.


Subdivision rules Hypercubes Simplicial Torus 

Mathematics Subject Classification (2010)

52C26 52B11 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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