Recovering the homology of immersed manifolds - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

Recovering the homology of immersed manifolds

Abstract

Given a sample of an abstract manifold immersed in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its tangent bundle---seen as subset of another Euclidean space---in a measure theoretic point of view, and in applying measure-based filtrations for persistent homology. The construction we propose is consistent and stable, and does not involve the knowledge of the dimension of the manifold. In order to obtain quantitative results, we introduce the normal reach, which is a notion of reach suitable for an immersed manifold.
Fichier principal
Vignette du fichier
ImmersedManifolds.pdf (2.03 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02396261 , version 1 (05-12-2019)
hal-02396261 , version 2 (09-12-2019)
hal-02396261 , version 3 (05-06-2020)

Identifiers

Cite

Raphaël Tinarrage. Recovering the homology of immersed manifolds. 2020. ⟨hal-02396261v3⟩
97 View
38 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More