Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

One-dimensional reduction of multidimensional persistent homology

Author(s): Francesca Cagliari; Barbara Di Fabio; Massimo Ferri
Journal: Proc. Amer. Math. Soc. 138 (2010), 3003-3017.
MSC (2010): Primary 55N99, 57R70, 58E17
Posted: April 9, 2010
MathSciNet review: 2644911
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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 the -essentiality of homological critical values conclude the paper.

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