A finite subdivision rule for the n-dimensional torus
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.
KeywordsSubdivision rules Hypercubes Simplicial Torus
Mathematics Subject Classification (2010)52C26 52B11
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