One-dimensional reduction of multidimensional persistent homology

@inproceedings{Cagliari2007OnedimensionalRO,
  title={One-dimensional reduction of multidimensional persistent homology},
  author={Francesca Cagliari and Barbara Di Fabio and Massimo Ferri},
  year={2007}
}
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. 
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