Homotopy Groups and Puppe Sequence of Digraphs
Algebraic Topology
2025-05-06 v4
Abstract
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, Muranov and Yau in 2014. This direct approach enables a descriptive interpretation of GLMY theory in applications such as network science. Furthermore, we prove that there exists a long exact sequence of homotopy groups of digraphs associated to any based digraph map, that is, there exists a digraph version of the Puppe sequence.
Cite
@article{arxiv.2402.01110,
title = {Homotopy Groups and Puppe Sequence of Digraphs},
author = {Jingyan Li and Jie Wu and Shing-Tung Yau and Mengmeng Zhang},
journal= {arXiv preprint arXiv:2402.01110},
year = {2025}
}