Abstract complexes, their homologies and applications
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CATARANCIUC, Sergiu, SOLTAN, Petru. Abstract complexes, their homologies and applications. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2010, nr. 2(63), pp. 31-58. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(63) / 2010 / ISSN 1024-7696 /ISSNe 2587-4322

Abstract complexes, their homologies and applications

Pag. 31-58

Cataranciuc Sergiu, Soltan Petru
 
Moldova State University
 
Disponibil în IBN: 6 decembrie 2013


Rezumat

The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods used for these constructions are for the most part analogous with classical methods [2,32,52], but sometimes they are based on methods from [18,44,58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.

Cuvinte-cheie
complex,

manifold, Abstract cube, quasi-simplex, multidimensional Euler tour