Persistent homology with non-contractible preimages

Konstantin Mischaikow; Charles Weibel

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arXiv · 2105.08130

Persistent homology with non-contractible preimages

Konstantin Mischaikow·Charles Weibel

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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).

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BibTeX RIS

Konstantin Mischaikow, Charles Weibel. 2021-05-17. Persistent homology with non-contractible preimages. https://arxiv.org/abs/2105.08130

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