Reference : Ephemeral persistence modules and distance comparison
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Ephemeral persistence modules and distance comparison
Berkouk, Nicolas mailto []
Petit, François mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Persitence module ; Persistent homology
[en] We provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of γ-sheaves. In the case of one-dimensional persistence, our definition agrees with the usual one showing that the observable category and the category of γ-sheaves are equivalent. We also establish isometry theorems between the category of persistent modules and γ-sheaves both endowed with their interleaving distance. Finally, we compare the interleaving and convolution distances.
FnR ; FNR5707106 > Martin Schlichenmaier > QUANTMOD > Quantization of Moduli Spaces > 01/09/2014 > 31/08/2017 > 2013

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