The Persistent Homology of a Self-Map

نویسندگان

  • Herbert Edelsbrunner
  • Grzegorz Jablonski
  • Marian Mrozek
چکیده

Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.

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عنوان ژورنال:
  • Foundations of Computational Mathematics

دوره 15  شماره 

صفحات  -

تاریخ انتشار 2015