Discrete Morse Theory on Digraphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Chong Wang School of Mathematics, Renmin University of China, Beijing 100872, China; School of Mathematics and Statistics, Cangzhou Normal University, 061000 China Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge MA 02138, USA

Combinatorics Algebraic Topology and General Topology mathscidoc:2207.06004

Pure and Applied Mathematics Quarterly
In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using quasi-isomorphism between path complex and discrete Morse complex, we also prove a general sufficient condition for digraphs that the Morse functions satisfying this necessary and sufficient condition.
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@inproceedings{yongdiscrete,
  title={Discrete Morse Theory on Digraphs},
  author={Yong Lin, Chong Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707155554882299574},
  booktitle={Pure and Applied Mathematics Quarterly},
}
Yong Lin, Chong Wang, and Shing-Tung Yau. Discrete Morse Theory on Digraphs. In Pure and Applied Mathematics Quarterly. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707155554882299574.
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