Stability of Reeb Ordering by Interleaving Distance
##article.authors##
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Tomoki Uda
Advanced Institute for Materials Research, Tohoku University
https://orcid.org/0000-0002-6073-1572
https://researchmap.jp/t_uda
DOI:
https://doi.org/10.51094/jxiv.519Keywords:
Reeb graph, Topological Data Analysis, interleaving distance, partially ordered spaceAbstract
The Reeb graph is instrumental in extracting topological features from contour plots. In this context, the Reeb ordering method offers both a natural discretisation and an algorithmic approach to compute a Reeb tree. Our main theorem establishes stability within the interleaving distance among order-compatible topological spaces. Our contributions are fourfold: we construct the reflector functor for quotient structures in ordered spaces, introduce generalised trees in poset terms, define branch completeness for graph-like posets, and prove a strong normalisation theorem for posets. Furthermore, our interleaving distance metric makes our stability estimate much finer than the preceding study.
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Submitted: 2023-10-03 08:14:07 UTC
Published: 2023-10-10 01:44:31 UTC
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Tomoki Uda
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