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A finite subdivision rule for the n-dimensional torus

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Temple University, 1805 N. Broad St., Philadelphia, PA, 19096, USA

    Brian Rushton

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  1. Brian Rushton
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Correspondence to Brian Rushton.

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Rushton, B. A finite subdivision rule for the n-dimensional torus. Geom Dedicata 167, 23–34 (2013). https://doi.org/10.1007/s10711-012-9802-5

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  • DOI: https://doi.org/10.1007/s10711-012-9802-5

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