This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.
@article{arxiv.1411.0613,
title = {Topological Data Analysis and Cosheaves},
author = {Justin Curry},
journal= {arXiv preprint arXiv:1411.0613},
year = {2015}
}
Comments
version 2 has 30 pages, 18 figures; 25 pages, 17 figures, submitted to the Japan Journal of Industrial and Applied Mathematics