A-infinity Persistence
Algebraic Topology
2017-06-20 v3 Computational Geometry
Computer Vision and Pattern Recognition
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.
Keywords
Cite
@article{arxiv.1403.2395,
title = {A-infinity Persistence},
author = {Francisco Belchí Guillamón and Aniceto Murillo Mas},
journal= {arXiv preprint arXiv:1403.2395},
year = {2017}
}
Comments
22 pages, no figures. In versions 2 and 3, we added our e-mail addresses and made some minor corrections, thanks to Jim Stasheff