Computing homology and persistent homology using iterated Morse decomposition
Algebraic Topology
2012-10-26 v2 Data Structures and Algorithms
Abstract
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph theoretical operations. We use iterated Morse decomposition, which allows us to sidetrack many problems related to the standard discrete Morse theory. In particular, this approach is provably correct in any dimension.
Cite
@article{arxiv.1210.1429,
title = {Computing homology and persistent homology using iterated Morse decomposition},
author = {Paweł Dłotko and Hubert Wagner},
journal= {arXiv preprint arXiv:1210.1429},
year = {2012}
}