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One-Dimensional Reduction of Multidimensional Persistent Homology

F. Cagliari·B. Di Fabio·M. Ferri
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Abstract

A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.

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F. Cagliari, B. Di Fabio, M. Ferri. 2008-07-28. One-Dimensional Reduction of Multidimensional Persistent Homology. https://arxiv.org/abs/math/0702713

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