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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

One-dimensional reduction of multidimensional persistent homology


Authors: Francesca Cagliari, Barbara Di Fabio and Massimo Ferri
Journal: Proc. Amer. Math. Soc. 138 (2010), 3003-3017
MSC (2010): Primary 55N99, 57R70, 58E17
Published electronically: April 9, 2010
MathSciNet review: 2644911
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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 $ i$-essentiality of homological critical values conclude the paper.


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Additional Information

Francesca Cagliari
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italia
Email: cagliari@dm.unibo.it

Barbara Di Fabio
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italia
Email: difabio@dm.unibo.it

Massimo Ferri
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italia
Email: ferri@dm.unibo.it

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10312-8
PII: S 0002-9939(10)10312-8
Received by editor(s): November 24, 2008
Received by editor(s) in revised form: November 30, 2009, and December 1, 2009
Published electronically: April 9, 2010
Communicated by: Paul Goerss
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.