A. Zomorodian, G. Carlsson, Computing Persistent Homology, Proc. Symp. Comput. Geom. (2004), pp. 347-356.
We study the homology of a filtered d-dimensional
simplicial complex K as a single algebraic entity and
establish a correspondence that
provides a simple description over fields.
Our analysis enables us to derive a natural
algorithm for computing persistent homology over
an arbitrary field in any dimension.
Our study also implies the lack of a simple
classification over non-fields.
Instead, we give an algorithm for computing individual
persistent homology groups over an arbitrary PIDs
in any dimension.
title = "Computing Persistent Homology",
author = "Zomorodian, A. and Carlsson, G.",
booktitle = "Proc. 20th Ann. ACM Sympos. Comput. Geom.",
year = 2004,
pages = 347--356,