Persistent homology with non-contractible preimages

DOI10.4310/HHA.2022.V24.N2.A16zbMATH Open1518.55005arXiv2105.08130MaRDI QIDQ6367870

Konstantin Mischaikow, Charles A. Weibel

Publication date: 17 May 2021

Abstract: For a fixed $N$, we analyze the space of all sequences $z=(z_1,dots,z_N)$, approximating a continuous function on the circle, with a given persistence diagram $P$, and show that the typical components of this space are homotopy equivalent to $S^1$. We also consider the space of functions on $Y$-shaped (resp., star-shaped) trees with a 2-point persistence diagram, and show that this space is homotopy equivalent to $S^1$ (resp., to a bouquet of circles).

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Classification of homotopy type (55P15)

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