Induced Matchings of Barcodes and the Algebraic Stability of Persistence

  title={Induced Matchings of Barcodes and the Algebraic Stability of Persistence},
  author={Ulrich Bauer and Michael Lesnick},
  booktitle={Symposium on Computational Geometry},
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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Decomposition of pointwise finite-dimensional persistence modules

  • W. Crawley-Boevey
  • Preprint
  • 2012
Highly Influential
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Corrections and supplementaries to my paper concerning Krull–Remak– Schmidt’s theorem

  • G. Azumaya
  • Nagoya Mathematical Journal, 1:117–124
  • 1950
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5 Excerpts

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