Publication
Optimising the topological information of the A∞-persistence groups
Journal Article (2019)
Journal
Discrete & Computational Geometry
Pages
29-54
Volume
62
Number
1
Doc link
https://doi.org/10.1007/s00454-019-00094-x
File
Authors
Abstract
Persistent homology typically studies the evolution of homology groups Hp(X) (with coefficients in a field) along a filtration of topological spaces. A∞-persistence extends this theory by analysing the evolution of subspaces such as V:=KerΔn|Hp(X)⊆Hp(X), where {Δm}m≥1 denotes a structure of A∞-coalgebra on H∗(X). In this paper we illustrate how A∞-persistence can be useful beyond persistent homology by discussing the topological meaning of V, which is the most basic form of A∞-persistence group. In addition, we explore how to choose A∞-coalgebras along a filtration to make the A∞-persistence groups carry more faithful information.
Categories
optimisation.
Author keywords
Persistent homology, Zigzag persistence, A∞-persistence, Topological data analysis, A∞-(co)algebras, Massey products, Knot theory, Rational homotopy theory, Spectral sequences
Scientific reference
F. Belchí. Optimising the topological information of the A∞-persistence groups. Discrete & Computational Geometry, 62(1): 29-54, 2019.
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