4 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 referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed…
Algebra of Path Integrals on Digraphs
Shing-Tung Yau, Mengmeng Zhang, Yunpeng Zi
In this paper, we extend the iterated integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated integrals on a digraph nat…
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…