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Path complexes and their homologies

A. A. Grigor’yan Department of Mathematics, University of Bielefeld, 33613, Bielefeld, Germany; Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia Yong Lin Department of Mathematics, Renmin University of China, Beijing, 100872, P.R. China Yu. V. Muranov Faculty of Mathematics and Computer Sciences, University of Warmia and Mazury, Olsztyn, Poland Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

TBD mathscidoc:2207.43007

Journal of Mathematical Sciences, 248, (5), 564–599, 2020.6
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 K¨unneth formulas for Cartesian product and join, which happen to be true at the level of chain complexes.
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@inproceedings{a.2020path,
  title={Path complexes and their homologies},
  author={A. A. Grigor’yan, Yong Lin, Yu. V. Muranov, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707153549833176565},
  booktitle={Journal of Mathematical Sciences},
  volume={248},
  number={5},
  pages={564–599},
  year={2020},
}
A. A. Grigor’yan, Yong Lin, Yu. V. Muranov, and Shing-Tung Yau. Path complexes and their homologies. 2020. Vol. 248. In Journal of Mathematical Sciences. pp.564–599. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707153549833176565.
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