A higher homotopic extension of persistent (co)homology
type: Item
instance of: scholarly article
title: A higher homotopic extension of persistent (co)homology
zbMATH Open document ID: 1405.55004
author: Estanislao Herscovich
published in: Journal of Homotopy and Related Structures
publication date: 2018-10-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1412.1871
review text: The authors consider the \(A_\infty\)-algebra structure on the cohomology of a dg algebra: the Rees dg algebra. They show that the cohomology obtained is precisely the complete persistent cohomology of the filtered simplicial set. This allows them to: {\parindent=6mm \begin{itemize}\item[-] define a new barcodes distance on the collection of all generalized barcodes to the \(A_\infty\)-algebra constructed before. They show that their metric generalizes the bottleneck distance and that it is invariant under quasi-isomorphisms of \(A_\infty\)-algebras, \item[-] prove, under more general hypotheses, the well known open problem that there is an equivalence between the restriction of the barcode of \(n\)-th type for the persistent cohomology and that of the \(n\)-th type for the persistent homology. \end{itemize}}
reviewed by: My Ismail Mamouni
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 16E45
Mathematics Subject Classification ID: 16W70
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 6953903
zbMATH Keywords: persistent homology
zbMATH Keywords: \(A_\infty\)-algebra
zbMATH Keywords: bottleneck distance
MaRDI profile type: Publication
OpenAlex ID: W2962841484
arXiv ID: 1412.1871
cites work: Q4023148
cites work: \(A_\infty\)-persistence
cites work: Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
cites work: A course in metric geometry
cites work: Knots
cites work: Size functions from a categorical viewpoint
cites work: Decomposition of pointwise finite-dimensional persistence modules
cites work: Persistent cohomology and circular coordinates
cites work: Dualities in persistent (co)homology
cites work: Encyclopedia of Distances
cites work: Q3514524
cites work: Q3655278
cites work: Topological persistence and simplification
cites work: Q4505020
cites work: A distance for similarity classes of submanifolds of a Euclidean space
cites work: Algebraic representation of size functions
cites work: Q4819371
cites work: Higher Koszul algebras and \(A\)-infinity algebras.
cites work: Using torsion theory to compute the algebraic structure of Hochschild (co)homology
cites work: Spectral sequences associated to deformations
cites work: Quotients of Completely Regular Spaces
cites work: ON THE HOMOLOGY THEORY OF FIBRE SPACES
cites work: Q3319420
cites work: \(A\)-infinity structure on Ext-algebras.
cites work: Exact couples in algebraic topology. I.-V
cites work: Q5614479
cites work: HIGHER ORDER LINKING NUMBERS
cites work: Rings with several objects
cites work: \(A_\infty\)-structures. Minimal Baues-Lemaire and Kadeishvili models and homology of fibrations
cites work: Q4424951
cites work: DG-algebras and derived A ∞-algebras
cites work: Filtered spaces admitting spectral sequence operations
cites work: Q3225387
cites work: Homotopy Associativity of H-Spaces. I
cites work: Q4296949
cites work: Q3102006
cites work: Degenerate random perturbations of Anosov diffeomorphisms
cites work: Computing persistent homology
DOI: 10.1007/S40062-017-0195-X
description: scientific article