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A-persistence

A-persistence
A-persistence
We introduce and study A∞-persistence on the homology, with coefficients in a field, of a filtration of topological spaces. This is a family, one for each n≥1, of homological invariants which provide information not readily available by the (persistent) Betti numbers of the given filtration. This may help to detect noise, not just in the simplicial structure of the filtration but in further geometrical properties in which the higher codiagonals of the A∞-structure are translated. Based in the classification of zigzag modules, a characterization of the A∞-persistence in terms of its associated barcode is given.
Persistent homology, A∞-persistence, A∞-coalgebra, Applied algebraic topology
0938-1279
121-139
Belchi Guillamon, Francisco
41c7c5e5-b259-45d8-89f9-7b7937517c53
Murillo, Aniceto
5dc85c68-9a81-4fce-8d94-0114e925eb44
Belchi Guillamon, Francisco
41c7c5e5-b259-45d8-89f9-7b7937517c53
Murillo, Aniceto
5dc85c68-9a81-4fce-8d94-0114e925eb44

Belchi Guillamon, Francisco and Murillo, Aniceto (2015) A-persistence. Applicable Algebra in Engineering, Communication and Computing, 26 (1), 121-139. (doi:10.1007/s00200-014-0241-4).

Record type: Article

Abstract

We introduce and study A∞-persistence on the homology, with coefficients in a field, of a filtration of topological spaces. This is a family, one for each n≥1, of homological invariants which provide information not readily available by the (persistent) Betti numbers of the given filtration. This may help to detect noise, not just in the simplicial structure of the filtration but in further geometrical properties in which the higher codiagonals of the A∞-structure are translated. Based in the classification of zigzag modules, a characterization of the A∞-persistence in terms of its associated barcode is given.

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More information

e-pub ahead of print date: 31 December 2014
Published date: March 2015
Keywords: Persistent homology, A∞-persistence, A∞-coalgebra, Applied algebraic topology
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 406898
URI: https://eprints.soton.ac.uk/id/eprint/406898
ISSN: 0938-1279
PURE UUID: 1cd8b365-b211-4774-b113-ec6ced4dbd95

Catalogue record

Date deposited: 25 Mar 2017 02:06
Last modified: 13 Mar 2019 20:13

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