2024/08/19 by Wayne A. Johnson, Johnson, Wayne A., Dae-Woong Lee +3
Computer Science · #05C30 #22A05 #55P45 #68U03 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2408.10087
openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 and NP2 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-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.