One-Dimensional Reduction of Multidimensional Persistent Homology

摘要

A recent result on size functions is extended to higher homology modules: the persistentudhomology based on a multidimensional measuring function is reduced to a 1-dimensionaludone. This leads to a stable distance for multidimensional persistent homology. Some reflec-udtions on i-essentiality of homological critical values conclude the paper.