English

On digital H-spaces

Algebraic Topology 2024-08-20 v1 Combinatorics

Abstract

In this article, we investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP1_1 and NP2_2 product adjacencies. We explore algebraic properties of digital H-spaces preserved under digital homotopy equivalence, and we give a general construction that produces examples of digital H-spaces which are not homotopy-equivalent to digital topological groups in both categories. Further, we show that this construction essentially classifies all NP2_2-digital H-spaces. In a short appendix, we resolve a question that was left unresolved in [17], and complete the full classification of digital topological groups.

Keywords

Cite

@article{arxiv.2408.10087,
  title  = {On digital H-spaces},
  author = {Wayne A. Johnson and Dae-Woong Lee and P. Christopher Staecker},
  journal= {arXiv preprint arXiv:2408.10087},
  year   = {2024}
}
R2 v1 2026-06-28T18:16:56.157Z