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# Induced Matchings of Barcodes and the Algebraic Stability of Persistence

@inproceedings{Bauer2014InducedMO, title={Induced Matchings of Barcodes and the Algebraic Stability of Persistence}, author={Ulrich Bauer and Michael Lesnick}, booktitle={Symposium on Computational Geometry}, year={2014} }

- Published 2014 in Symposium on Computational Geometry
DOI:10.1145/2582112.2582168

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.
As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of… CONTINUE READING

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