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.File in questo prodotto:
Eventuali allegati, non sono esposti
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.