An Exposition on the Algebra and Computation of Persistent Homology
Algebraic Topology
2024-08-16 v1
Abstract
We discuss the algebra behind the matrix reduction algorithm for persistent homology, as presented in the paper ''Computing Persistent Homology'' by Afra Zomorodian and Gunnar Carlsson, in the lens of the more modern characterization of persistence modules as functors from a poset category to a category of vector spaces over a field adopted by authors such as Peter Bubenik, Frederik Chazal, and Ulrich Bauer.
Keywords
Cite
@article{arxiv.2408.07899,
title = {An Exposition on the Algebra and Computation of Persistent Homology},
author = {Jason Ranoa},
journal= {arXiv preprint arXiv:2408.07899},
year = {2024}
}
Comments
Expository Paper for MS Degree in Math at Oregon State University. Edited by Dr. Christine Escher (advisor)