Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Discrete Morse theory on digraphs
Pages: 1711 – 1737
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.
discrete Morse theory, quasi-isomorphism, path homology
2010 Mathematics Subject Classification
Yong Lin was partially supported by National Natural Science Foundation of China, Grant No. 12071245.
Chong Wang was partially supported by Science and Technology Project of Hebei Education Department (QN2019333), by the Natural Fund of Cangzhou Science and Technology Bureau (No. 197000002), and by a Project of Cangzhou Normal University (No. xnjjl1902).
Shing-Tung Yau was partially supported by DMS-1737873.
Received 29 January 2021
Accepted 25 May 2021
Published 26 January 2022