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arXiv · 2610.20046

Real Tree Vineyards have Vines

Michael Hull·Thomas Payne·Thomas Weighill
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Abstract

We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams $\mathcal{D}$ can be decomposed into a sequence of paths in $\mathbb R^2$. Moreover, we characterize which spaces $X$ have the property that every continuous map $X\to \mathcal{D}$ has such a decomposition. Our results hold not just for $\mathcal{D}$, but also for many other spaces of unordered tuples.

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Michael Hull, Thomas Payne, Thomas Weighill. 2026-10-14. Real Tree Vineyards have Vines. https://arxiv.org/abs/2610.20046

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