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arXiv · 1805.02539

Persistent Local Systems

Robert MacPherson·Amit Patel
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Abstract

In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under perturbations of the map. This generalizes certain ideas of persistent homology to higher dimensions.

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BibTeXRIS

Robert MacPherson, Amit Patel. 2018-05-07. Persistent Local Systems. https://doi.org/10.1016/j.aim.2021.107795

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