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IMCS/Publications/BASM/Issues/BASM n.2 (51), 2006/

On the Division of Abstract Manifolds in Cubes.

Authors: Mariana Bujac, Sergiu Cataranciuc, Petru Soltan

Abstract

We prove that in the class of abstract multidimensional manifolds without borders only torus Vnn of dimension n ≥ 1 can be divided in abstract cubes with the property: every face Im from Vnn is shared by 2n-m cubes, m=0, 1, ..., n-1. The abstract torus V1n is realized in Ed, n + 1 ≤ d ≤ 2n + 1 so it results that in the class of all n-dimensional combinatorial manifolds [1] only torus respects this propriety. Torus is autodual because of this propriety.

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