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arXiv · 2208.14063

Minimal Path and Acyclic Models in the Path Complex

Xinxing Tang·Shing-Tung Yau
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Abstract

In this paper, firstly, we will study the structure of the path complex $(\Omega_*(G;\Z),\partial)$ of a digraph $G$ via the $\Z$-generators of $\Omega_*(G,\Z)$ under strongly regular condition, which is called the minimal path in \cite{HY}. In particular, we will study various examples of the minimal $3$-paths. Secondly, we will show that the supporting sub-digraph of minimal path has acyclic path homologies. Thirdly, we will consider the applications of such an acyclic model.

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Xinxing Tang, Shing-Tung Yau. 2022-08-30. Minimal Path and Acyclic Models in the Path Complex. https://arxiv.org/abs/2208.14063

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