From the 1 of 43 linked papers with an AI index.
7 papers · 1 filter
A Sharp Curvature Threshold for GLMY Path Homology
Shuliang Bai, Jingyan Li, Shing-Tung Yau
Let be a finite simple graph with at least one edge. We prove the sharp vanishing theorem \[ κ_{\min}^{\mathrm{LLY}}(G)>\frac12 \quad\Longrightarrow\quad \PathH_1(G;\R)=0. \] E…
Szczarba's twisted shuffle and equivariant path homology of directed graphs
Xin Fu, Shing-Tung Yau
To a marked simplicial set one can associate its path chain complex, and define its homology to be the homology of this complex, inspired by path homology theories for directed gra…
Computing singular simplicial homologies of digraphs and quivers
Matthew Burfitt, Jie Wu, Stephen S. -T. Yau +1
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver…
Minimal Path and Acyclic Models in the Path Complex
Xinxing Tang, Shing-Tung Yau
In this paper, firstly, we will study the structure of the path complex of a digraph via the -generators of under strongly regular cond…
Homotopy Groups and Puppe Sequence of Digraphs
Jingyan Li, Jie Wu, Shing-Tung Yau +1
We introduce homotopy groups of digraphs that admit an intuitive description of grid structures, which is a variation of the GLMY homotopy groups introduced by Grigor'yan, Lin, Mur…
Calculating Higher Digraph Homotopy Groups
Stephen Theriault, Jie Wu, Shing-Tung Yau +1
We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this we define relative digraph homotopy groups and show these satisfy a lon…