The fiber of persistent homology for trees

David Beers; Jacob Leygonie

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arXiv · 2303.16176

The fiber of persistent homology for trees

David Beers·Jacob Leygonie

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Abstract

Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homotopy equivalent to a configuration space on $X$ with specialized constraints encoded by the merge tree. For barcodes $D$ with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.

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David Beers, Jacob Leygonie. 2023-03-28. The fiber of persistent homology for trees. https://arxiv.org/abs/2303.16176

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