Induced Matchings of Barcodes and the Algebraic Stability of Persistence
Ulrich Bauer, Michael Lesnick · 2014
We define a simple, explicit map sending a morphism f: M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f.