One-Dimensional Reduction of Multidimensional Persistent Homology

Details One-Dimensional Reduction of Multidimensional Persistent Homology One-Dimensional Reduction of Multidimensional Persistent Homology

2007-02-23

arxiv.org/abs/math/0702713v2

Mathematics

Algebraic Topology

16 pages, 11 figures

Scientific paper

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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