On the Stability of Interval Decomposable Persistence Modules
Peer reviewed, Journal article
Published version
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Date
2021Metadata
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- Institutt for matematiske fag [2350]
- Publikasjoner fra CRIStin - NTNU [37177]
Original version
Discrete & Computational Geometry. 2021, 66 (1), 92-121. 10.1007/s00454-021-00298-0Abstract
The algebraic stability theorem for persistence modules is a central result in the theory of stability for persistent homology. We introduce a new proof technique which we use to prove a stability theorem for n-dimensional rectangle decomposable persistence modules up to a constant 2n−1 that generalizes the algebraic stability theorem, and give an example showing that the bound cannot be improved for n=2. We then apply the technique to prove stability for block decomposable modules, from which novel results for zigzag modules and Reeb graphs follow. These results are improvements on weaker bounds in previous work, and the bounds we obtain are optimal.