3 papers
math.AT2026
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…
math.AT2026
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…
math.AT2025
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…