# Stable Comparison of Multidimensional Persistent Homology Groups with Torsion

@article{Frosini2010StableCO,
title={Stable Comparison of Multidimensional Persistent Homology Groups with Torsion},
author={Patrizio Frosini},
journal={Acta Applicandae Mathematicae},
year={2010},
volume={124},
pages={43-54}
}
• P. Frosini
• Published 19 December 2010
• Mathematics
• Acta Applicandae Mathematicae
The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a pseudo-distance dT that represents a possible solution to this problem. Indeed, dT is a pseudo-distance between multidimensional persistent homology groups with coefficients in an Abelian group, hence possibly having torsion. Our main theorem proves the stability of the…
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