\(A_\infty\) persistent homology estimates detailed topology from pointcloud datasets. (English) Zbl 1496.55005
In the study of pointcloud datasets, describing topological properties of the underlying spaces \(X\) has proven to be beneficial. Up to date there are many techniques that study and compute the Betti numbers of \(X\) from a finite set \(P\) of points approximating \(X\).
In this paper much more detailed topological properties of \(X\) are studied utilizing the techniques of \(A_\infty\)-persistent homology. As a consequence, the stability of cup products and generalised Massey products in persistent homology has been proved.
In this paper much more detailed topological properties of \(X\) are studied utilizing the techniques of \(A_\infty\)-persistent homology. As a consequence, the stability of cup products and generalised Massey products in persistent homology has been proved.
Reviewer: Jelena Grbić (Southampton)
MSC:
| 55N31 | Persistent homology and applications, topological data analysis |
| 62-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics |
| 68U01 | General topics in computing methodologies |
| 55Uxx | Applied homological algebra and category theory in algebraic topology |
Keywords:
linking number; Betti numbers; cup product; persistent homology; topological data analysis (TDA); functoriality; Massey products; loop spaces; formal spaces; geometric estimation; bottleneck distance; interleaving distance; applied algebraic topology; stability; \(A_\infty\)-algebra; persistent cohomology; topological estimation; \(A_\infty\)-coalgebra; \(A_\infty\)-persistent homology; \(A_\infty\)-persistenceReferences:
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