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The aim is to explore the Lp-Vietoris-Rips complex and its properties across different values of p from 1 to infinity.

On ₚ-Vietoris-Rips complexes

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The aim is to explore the Lp-Vietoris-Rips complex and its properties across different values of p from 1 to infinity.
Analysis of Lp-Vietoris-Rips simplicial set and complex as p varies from 1 to infinity.
Proof of stability theorem for persistent homology relevant to Lp complexes.
Investigation of homotopy equivalence in compact Riemannian manifolds.
Establishes stability for persistent homology across Lp-Vietoris-Rips complexes.
All Lp-Vietoris-Rips spaces are homotopy equivalent to the compact manifold for small scale parameters.
Demonstrates invariance under metric completion and that limit of homology groups does not depend on p.

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Demonstrates properties of Lp-Vietoris-Rips complexes, indicating their utility in metric space analysis.

Ivanov et al. (2026) studied this question.

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