One-Dimensional Reduction of Multidimensional Persistent Homology
arXiv:math/0702713
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.
16 pages, 11 figures