On the Division of Abstract Manifolds in Cubes
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BUJAC, Mariana; CATARANCIUC, Sergiu; SOLTAN, Petru. On the Division of Abstract Manifolds in Cubes. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2006, nr. 2(51), pp. 29-34. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(51) / 2006 / ISSN 1024-7696

On the Division of Abstract Manifolds in Cubes

Pag. 29-34

Bujac Mariana, Cataranciuc Sergiu, Soltan Petru
 
State University of Moldova
 
Disponibil în IBN: 18 decembrie 2015


Rezumat

We prove that in the class of abstract multidimensional manifolds without borders only torus V n 1 of dimension n ≥ 1 can be divided in abstract cubes with the property: every face Im from V n 1 is shared by 2n−m cubes, m = 0, 1, . . . , n − 1. The abstract torus V n 1 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.

Cuvinte-cheie
Abstract manifold, abstract cubic manifold, cubiliaj, Euler characteristic.