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arXiv · 1604.03596

Parametrized Homology via Zigzag Persistence

Gunnar Carlsson·Vin de Silva·Sara Kalisnik·Dmitriy Morozov
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Abstract

This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or, equivalently, as a persistence diagram. By defining persistence in terms of finite rectangle measures, we classify barcode intervals into four classes. Each of these conveys how the homological features perish at both ends of the interval over which they are defined.

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Gunnar Carlsson, Vin de Silva, Sara Kalisnik, Dmitriy Morozov. 2016-04-12. Parametrized Homology via Zigzag Persistence. https://doi.org/10.2140/agt.2019.19.657

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