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This is a video about Algebraic Stability of Zigzag Persistence Modules

Algebraic Stability of Zigzag Persistence Modules

May 17, 2016
MBI
Presenters: Michael Lesnick
Length: 48 minutes 52 seconds

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Abstract

The stability theorem for persistent homology is a central result in topological data analysis.

While the original formulation of the result concerns the persistent homology of mathbb{R}-

valued functions, the result was later cast in a more general algebraic form, in the language of

persistence modules and interleavings. In this work, we establish an analogue of this algebraic

stability theorem for zigzag persistence modules. To do so, we functorially extend each zigzag

persistence module to a two-dimensional persistence module, and establish an algebraic stability

theorem for these extensions. As an application of our main theorem, we strengthen a result of

Bauer, Munch, and Wang on the stability of the persistent homology of Reeb graphs. Our main

result also yields an alternative proof of the stability theorem for level set persistent homology of

Carlsson et al.

This is joint work with Magnus Botnan.