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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 224–237 (Mi smj1836)  
This article is cited in 11 scientific papers (total in 11 papers)

Homology groups of semicubical sets

A. A. Khusainov

Komsomolsk-on-Amur State Technical University
Full-text PDF (349 kB) Citations (11)
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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.
Keywords: cubical homology, homology of a small category, semicubical sets, Serre spectral sequence.
Received: 09.10.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 1, Pages 180–190
DOI: https://doi.org/10.1007/s11202-008-0019-7
Bibliographic databases:
UDC: 512.66
Language: Russian
Citation: A. A. Khusainov, “Homology groups of semicubical sets”, Sibirsk. Mat. Zh., 49:1 (2008), 224–237; Siberian Math. J., 49:1 (2008), 180–190
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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