# Computing Persistent Homology

@article{Zomorodian2004ComputingPH,
title={Computing Persistent Homology},
author={Afra Zomorodian and Gunnar E. Carlsson},
journal={Discrete \& Computational Geometry},
year={2004},
volume={33},
pages={249-274}
}
• Published 8 June 2004
• Mathematics, Computer Science
• Discrete & Computational Geometry
Abstract We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This result generalizes and extends the previously known algorithm…
993 Citations

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