# The Theory of the Interleaving Distance on Multidimensional Persistence Modules

@article{Lesnick2015TheTO,
title={The Theory of the Interleaving Distance on Multidimensional Persistence Modules},
author={Michael Lesnick},
journal={Foundations of Computational Mathematics},
year={2015},
volume={15},
pages={613-650}
}
• M. Lesnick
• Published 26 June 2011
• Mathematics
• Foundations of Computational Mathematics
In 2009, Chazal et al. introduced $$\epsilon$$ϵ-interleavings of persistence modules. $$\epsilon$$ϵ-interleavings induce a pseudometric $$d_\mathrm{I}$$dI on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $$\epsilon$$ϵ-interleavings and $$d_\mathrm{I}$$dI generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view toward applications to topological data analysis…
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