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Homology groups of semicubical sets

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Abstract

We study the homology groups of semicubical sets with coefficients in the homological systems of abelian groups. The main theorem states that the groups under consideration are isomorphic to the homology groups of the category of singular cubes. This yields an isomorphism criterion for the homology groups of semicubical sets, the spectral sequence of a locally directed covering, and the spectral sequence of a morphism of semicubical sets.

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Authors and Affiliations

  1. Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur, Russia

    A. A. Khusainov

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  1. A. A. Khusainov
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Correspondence to A. A. Khusainov.

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Original Russian Text Copyright © 2008 Khusainov A. A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 224–237, January–February, 2008.

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Khusainov, A.A. Homology groups of semicubical sets. Sib Math J 49, 180–190 (2008). https://doi.org/10.1007/s11202-008-0019-7

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  • DOI: https://doi.org/10.1007/s11202-008-0019-7

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