# Recovering the homology of immersed manifolds

arXiv: https://arxiv.org/abs/1912.03033 · HTML: https://mlsanity.com/paper/1912.03033/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [Tangent Space and Dimension Estimation with the Wasserstein Distance](https://mlsanity.com/paper/2110.06357/) (2021)
- [Topological Point Cloud Clustering](https://mlsanity.com/paper/2303.16716/) (2023)
- [LieDetect: Detection of representation orbits of compact Lie groups from point clouds](https://mlsanity.com/paper/2309.03086/) (2023)

## Abstract (arXiv)

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.