nLab discrete homotopy theory

Idea

Discrete homotopy theory (also known as A-homotopy theory) is an area of mathematics concerned with using techniques of homotopy theory to study combinatorial properties of graphs. It does so by introducing a new combinatorial notion of homotopy between graph maps and subsequently reinterpreting the usual homotopy-theoretic invariants, such as homotopy or homology groups, through the lenses of this new notion.

References

• Hélène Barcelo, Reinhard Laubenbacher, Perspectives on A-homotopy theory and its applications, Discrete Mathematics 298 (2005), no. 1-3, 39–61.

• Rachel Hardeman Morrill, The Lifting Properties of A-Homotopy Theory [arXiv:1904.12065]

• Chris Kapulkin, Udit Mavinkurve, The fundamental group(oid) in discrete homotopy theory [arXiv:2303.06029]