One-dimensional reduction of multidimensional persistent homology

By F. Cagliari, B. D. Fabio, Massimo Ferri. 2007

53 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e1fee22c4150ae5fae79d08ce3a6d5eea5793ab

Citations in the corpus

• Betti numbers in multidimensional persistent homology are stable functions (2013, unknown): “Such a result has been partially extended in [3] for al l homology degrees, under the restrictive assumption that the vector-valued filterin g functions aremax-tame.”
• Proximity of persistence modules and their diagrams (2009, unknown): “Stability results for this descriptor exist in several restricted contexts [3, 4], and it would be interesting to see whether they can be extended to a larger setting similar to the one of this paper.”