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arXiv · 2111.04527

Determining homology of an unknown space from a sample

Morten Brun·Belén García Pascual·Lars M. Salbu
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Abstract

The homology of an unknown subspace of Euclidean space can be determined from the intrinsic \v{C}ech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace $X$ of Euclidean space and a sample $A$ of points in $X$, we give conditions for the homology of $X$ to be isomorphic to a certain persistent homology group of the intrinsic \v{C}ech complex.

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Morten Brun, Belén García Pascual, Lars M. Salbu. 2021-11-08. Determining homology of an unknown space from a sample. https://arxiv.org/abs/2111.04527

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