Publication
A∞ Persistent Homology Estimates Detailed Topology from Pointcloud Datasets
Journal Article (2022)
Journal
Discrete & Computational Geometry
Pages
274-297
Volume
68
Doc link
http://dx.doi.org/10.1007/s00454-021-00319-y
File
Abstract
Let X be a closed subspace of a metric space M. It is well known that, under mild hypotheses, one can estimate the Betti numbers of X from a finite set P⊂M of points approximating X. In this paper, we show that one can also use P to estimate much more detailed topological properties of X. We achieve this by proving the stability of A∞-persistent homology. In its most general case, this stability means that given a continuous function f:Y→R on a topological space Y, small perturbations in the function f imply at most small perturbations in the family of A∞-barcodes. This work can be viewed as a proof of the stability of cup-product and generalized-Massey-products persistence. The technical key of this paper consists of figuring out a setting which makes A∞-persistence functorial.
Categories
optimisation.
Scientific reference
F. Belchí and A. Stefanou. A∞ Persistent Homology Estimates Detailed Topology from Pointcloud Datasets. Discrete & Computational Geometry, 68: 274-297, 2022.
Follow us!