Recovering the homology of immersed manifolds

Raphaël Tinarrage

doi:10.1007/s00454-022-00409-5

Article Dans Une Revue Discrete and Computational Geometry Année : 2023

Recovering the homology of immersed manifolds

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Raphaël Tinarrage

Fonction : Auteur
PersonId : 737674
IdHAL : raphael-tinarrage
ORCID : 0000-0002-1404-1095
IdRef : 250339056

Understanding the Shape of Data

Laboratoire de Mathématiques d'Orsay

Résumé

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.

Domaines

Géométrie algorithmique [cs.CG] Géométrie différentielle [math.DG]

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Raphaël Tinarrage : Connectez-vous pour contacter le contributeur

https://hal.science/hal-02396261

Soumis le : mardi 2 avril 2024-19:19:03

Dernière modification le : vendredi 26 avril 2024-13:04:07

Dates et versions

hal-02396261 , version 1 (05-12-2019)

hal-02396261 , version 2 (09-12-2019)

hal-02396261 , version 3 (05-06-2020)

hal-02396261 , version 4 (02-04-2024)

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Paternité

Identifiants

HAL Id : hal-02396261 , version 4
ARXIV : 1912.03033
DOI : 10.1007/s00454-022-00409-5

Citer

Raphaël Tinarrage. Recovering the homology of immersed manifolds. Discrete and Computational Geometry, 2023, 69 (3), pp.659-744. ⟨10.1007/s00454-022-00409-5⟩. ⟨hal-02396261v4⟩

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Recovering the homology of immersed manifolds

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