descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 31 Dec 2014Embargo end date: 01 Jan 2014 English Publisher:Springer Science and Business Media LLCJournal:Applicable Algebra in Engineering, Communication and Computing, volume 26, pages 121-139 (issn: 0938-1279, eissn: 1432-0622,

Authors: Belchi Guillamon, Francisco; Murillo, Aniceto;

doi: 10.1007/s00200-014-0241-4 , 10.48550/arxiv.1403.2395

arXiv: http://arxiv.org/abs/1403.2395

$$A_\infty $$ A ∞ -persistence

- Summary
- Subjects
- Metrics

Abstract

We introduce and study A-infinity persistence of a given homology filtration of topological spaces. This is a family, one for each n > 0, 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-infinity structure are translated. Based in the classification of zigzag modules, a characterization of the A-infinity persistence in terms of its associated barcode is given.

22 pages, no figures. In versions 2 and 3, we added our e-mail addresses and made some minor corrections, thanks to Jim Stasheff

Related Organizations

University of Malaga
Spain
University of Southampton
United Kingdom

Keywords

Computational Geometry (cs.CG), FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, FOS: Mathematics, 500, Computer Science - Computational Geometry, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 510

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	8
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average