Recovering the Homology of Immersed Manifolds

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—from a measure theoretical point of view, and in applying measu...

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Bibliographic Details
Published in:Discrete & computational geometry 2023-04, Vol.69 (3), p.659-744
Main Author: Tinarrage, Raphaël
Format: Article
Language:English
Subjects:
Algorithms
Bar codes
Combinatorics
Computational Geometry
Computational Mathematics and Numerical Analysis
Computer Science
Differential Geometry
Euclidean geometry
Euclidean space
Geometry
Homology
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
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Summary: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—from a measure theoretical point of view, and in applying measure-based filtrations for persistent homology. The construction we propose is consistent and stable, and does not require the dimension of the manifold.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-022-00409-5