On digital H-spaces

Wayne A. Johnson; Dae-Woong Lee; P. Christopher Staecker

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arXiv · 2408.10087

On digital H-spaces

Wayne A. Johnson·Dae-Woong Lee·P. Christopher Staecker

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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$_1$ and NP$_2$ 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 NP$_2$-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.

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BibTeX RIS

Wayne A. Johnson, Dae-Woong Lee, P. Christopher Staecker. 2024-08-19. On digital H-spaces. https://arxiv.org/abs/2408.10087

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