The Persistent Homology of a Self-Map
نویسندگان
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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ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 15 شماره
صفحات -
تاریخ انتشار 2015