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Fundamentalnaya i Prikladnaya Matematika, 2016, Volume 21, Issue 5, Pages 79–128 (Mi fpm1759)  
This article is cited in 34 scientific papers (total in 34 papers)

Path complexes and their homologies

A. A. Grigor'yanab, Yong Linc, Yu. V. Muranovd, Shing-Tung Yaue

a Department of Mathematics, University of Bielefeld, 33613 Bielefeld, Germany
b Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
c Department of Mathematics, Renmin University of China, Beijing 100872, P.R. China
d Faculty of Mathematics and Computer Sciences, University of Warmia and Mazury, Olsztyn, Poland
e Department of Mathematics, Harvard University, Cambridge MA 02138, USA
Full-text PDF (1626 kB) Citations (34)
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Abstract: We introduce the notions of a path complex and its homologies. Particular cases of path homologies are simplicial homologies and digraph homologies. We state and prove some properties of path homologies, in particular, the Künneth formulas for Cartesian product and join, which happen to be true at the level of chain complexes.
Funding agency Grant number
Deutsche Forschungsgemeinschaft SFB 701
Research Funds of Renmin University of China 11XNI004
Air Force Office of Scientific Research FA-9550-13-1-0097
The first author was partially supported by SFB 701 of the German Research Council, Visiting Grants of Harvard University, and MSC of Tsinghua University. The second author was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (11XNI004). The third author was partially supported by SFB 701 of the German Research Council. The fourth author was partially supported by the grant “Geometry and Topology of Complex Networks,” No. FA-9550-13-1-0097.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 5, Pages 564–599
DOI: https://doi.org/10.1007/s10958-020-04897-9
Document Type: Article
UDC: 512.66+519.17
Language: Russian
Citation: A. A. Grigor'yan, Yong Lin, Yu. V. Muranov, Shing-Tung Yau, “Path complexes and their homologies”, Fundam. Prikl. Mat., 21:5 (2016), 79–128; J. Math. Sci., 248:5 (2020), 564–599
Citation in format AMSBIB
\Bibitem{GriLinMur16}
\by A.~A.~Grigor'yan, Yong~Lin, Yu.~V.~Muranov, Shing-Tung~Yau
\paper Path complexes and their homologies
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 5
\pages 79--128
\mathnet{http://mi.mathnet.ru/fpm1759}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 248
\issue 5
\pages 564--599
\crossref{https://doi.org/10.1007/s10958-020-04897-9}
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  • https://www.mathnet.ru/eng/fpm/v21/i5/p79
    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Фундаментальная и прикладная математика
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