The ANR version of Hausmann's theorem for Vietoris-Rips complexes
Let be a compact ANR metric space, where ANR means an absolute neighborhood retract. Let denote the Vietoris-Rips complex at scale .
ANR Vietoris-Rips conjecture. There exists such that
for every .
This is proposed as a version of Hausmann's theorem for compact ANR metric spaces. The source does not state whether the conjecture has been resolved.
References
Primary source
Sunhyuk Lim, Facundo Memoli and Osman Berat Okutan, “Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius”, arXiv:2001.07588 (2024).
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