Cubical setting for discrete homotopy theory, revisited
Combinatorics
2025-12-23 v3 Algebraic Topology
Category Theory
Abstract
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use this to prove a conjecture of Babson, Barcelo, de Longueville, and Laubenbacher from 2006, and a strong version of the Hurewicz theorem in discrete homotopy theory.
Cite
@article{arxiv.2202.03516,
title = {Cubical setting for discrete homotopy theory, revisited},
author = {Daniel Carranza and Chris Kapulkin},
journal= {arXiv preprint arXiv:2202.03516},
year = {2025}
}
Comments
version accepted for publication