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.

Cagliari F., Di Fabio B., Ferri M. (2010). One-dimensional reduction of multidimensional persistent homology. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138, 3003-3017 [10.1090/S0002-9939-10-10312-8].

One-dimensional reduction of multidimensional persistent homology

CAGLIARI, FRANCESCA;DI FABIO, BARBARA;FERRI, MASSIMO
2010

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.
2010
Cagliari F., Di Fabio B., Ferri M. (2010). One-dimensional reduction of multidimensional persistent homology. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138, 3003-3017 [10.1090/S0002-9939-10-10312-8].
Cagliari F.; Di Fabio B.; Ferri M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/81512
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