5 citations · 5 across the 5 of their papers we have counts for
6 papers
The discrete homotopy hypothesis for directed graphs
Briony Eldridge, Sergei O. Ivanov, Xiaomeng Xu +2
We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as -groups or reduced GLMY homotopy groups. Localizing the category of directed grap…
Algebra of Path Integrals on Digraphs
Shing-Tung Yau, Mengmeng Zhang, Yunpeng Zi
In this paper, we extend the iterated path integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated path integrals on a d…
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…
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…
On the path homology of Cayley digraphs and covering digraphs
Shaobo Di, Sergei O. Ivanov, Lev Mukoseev +1
We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group ho…
The Embedded Homology of Hypergraph Pairs
Shiquan Ren, Jie Wu, Mengmeng Zhang
In this paper, we generalize the embedded homology groups of hypergraphs initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology of hypergraphs and applicat…