Dualities in persistent (co)homology
Algebraic Topology
2015-05-28 v1 Computational Geometry
Abstract
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. We present experimental evidence for the practical efficiency of the latter algorithm.
Cite
@article{arxiv.1107.5665,
title = {Dualities in persistent (co)homology},
author = {Vin de Silva and Dmitriy Morozov and Mikael Vejdemo-Johansson},
journal= {arXiv preprint arXiv:1107.5665},
year = {2015}
}
Comments
16 pages, 3 figures, submitted to the Inverse Problems special issue on Topological Data Analysis