有向图及其道路同调的△集刻画

Simplicial Descriptions for Digraphs and Their Path Homology from the Point of Δ-sets

近几年来,A.Grigor’yan,Y.Lin,Y.Muranov,V.Vershinin和S.T.Yau等人研究了有向图上的道路,定义了有向图的道路同调并将其作为重要的代数工具来研究有向图的拓扑结构.将有向图上的道路集合描述为△集的分次子集,通过推广超图的嵌入同调定义△集的分次子集的嵌入同调并证明有向图的道路同调可以描述为△集的分次子集的嵌入同调.

In recent years,paths on digraphs were studied by A.Grigor’yan,Y.Lin,Y.Muranov,V.Vershinin and S.T.Yau,and the path homology was invented as an algebraic tool for the topology of digraphs.In this talk,we describe the sets of paths on digraphs as graded subsets of A-sets.By generalizing the embedded homology of hypergraphs and define the embedded homology of graded subsets of△-sets,we prove that path homology of digraphs can be described as the embedded homology of graded subsets of△-sets.