, Volume 167, Issue 1, pp 23-34
Date: 27 Nov 2012

A finite subdivision rule for the n-dimensional torus

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.