Recovering the homology of immersed manifolds

12/06/2019

∙

by   Raphaël Tinarrage, et al.

∙

0

∙

share

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.