2026-09-30T02:35:14Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25889 2026-09-23T23:53:43Z ddc:004 open_access

A Persistent Version of Latschev’s Theorem Oudot, Steve Waas, Lukas Topological data analysis (TDA) metric geometry Vietoris-Rips complex homotopy theory multi-parameter persistent homology Latschev’s theorem provides sufficient conditions on a metric space M and δ > 0 for the homotopy type of M to agree with that of the Vietoris-Rips complex ℛ^δ(𝕄) of any nearby space 𝕄 in the Gromov-Hausdorff distance. We prove a persistent version of this theorem, providing sufficient conditions on a pair (M, f:M → ℝ^N) and δ > 0 for the persistent homotopy type of the sublevel set filtration of (M, f) to be interleaved with that of the function-Rips complex ℛ^δ(𝕄^•) of any nearby pair (𝕄, 𝕗). In particular, our result answers a longstanding question on the related topic of estimating sublevel set persistent homology from finite point samples. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Steve Oudot and Lukas Waas 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.82 urn:nbn:de:0030-drops-258891 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.82 eng https://creativecommons.org/licenses/by/4.0/legalcode