One-dimensional reduction of multidimensional persistent homology
Francesca Cagliari, Barbara Di Fabio, Massimo Ferri · Proceedings of the American Mathematical Society · 2010
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 i -essentiality of homological critical values conclude the paper.