Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hull, Michael, Payne, Thomas, Weighill, Thomas
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222144796