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arXiv · 2305.03357

Persistent homology of partially ordered spaces

Cameron Calk·Eric Goubault·Philippe Malbos
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Abstract

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was developed in the context of topological data analysis, in which topological properties of point-cloud data sets are extracted while eliminating noise. In both approaches, the evolution homological properties are tracked through a sequence of inclusions of usual topological spaces. Exploiting this similarity, we show that natural homology may be considered a persistence object, and may be calculated as a colimit of uni-dimensional persistent homologies along traces. Finally, we suggest further links and avenues of future work in this direction.

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Cameron Calk, Eric Goubault, Philippe Malbos. 2023-05-05. Persistent homology of partially ordered spaces. https://arxiv.org/abs/2305.03357

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