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 NP and NP 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 NP-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.
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}
}