One-Dimensional Reduction of Multidimensional Persistent Homology

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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.
16 pages, 11 figures

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Algebraic Topology, 55N20; 68U05

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http://salesiana.dossiersoluciones.com/handle/123456789/165808

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702713
 http://arxiv.org/abs/math/0702713

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arXiv