Calculating Higher Digraph Homotopy Groups

2025/04/05 by Theriault, Stephen, Wu, Jie, Yau, Shing-Tung +1
#05C20 #55Q05 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.04119

Abstract

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 long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs.

Related

• Homotopy theory for digraphs
• The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs
• Homotopy Groups and Puppe Sequence of Digraphs
• Higher discrete homotopy groups of graphs
• Modelling and Computing Homotopy Types: I