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PreprintarXiv licencearXiv

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 𝒟 can be decomposed into a sequence of paths in ℝ2. Moreover, we characterize which spaces X have the property that every continuous map X→ 𝒟 has such a decomposition. Our results hold not just for 𝒟, but also for many other spaces of unordered tuples.

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Cite

BibTeXRIS
BibTeX
@misc{hull2026real,
  title = {{Real Tree Vineyards have Vines}},
  author = {Michael Hull and Thomas Payne and Thomas Weighill},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20046},
  eprint = {2610.20046},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20046},
}
RIS
TY  - UNPB
TI  - Real Tree Vineyards have Vines
AU  - Michael Hull
AU  - Thomas Payne
AU  - Thomas Weighill
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20046
UR  - https://arxiv.org/abs/2610.20046
AB  - We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams 𝒟 can be decomposed into a sequence of paths in ℝ^2. Moreover, we characterize which spaces X have the property that every continuous map X→ 𝒟 has such a decomposition. Our results hold not just for 𝒟, but also for many other spaces of unordered tuples.
ER  -