Persistent Local Systems

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.

This is the final version of the paper. It appears in Advances in Mathematics

References in corpus (2)

• Generalized Persistence Diagrams
• Classification of Constructible Cosheaves

Cited by in corpus (3)

• Harder-Narasimhan Filtrations of Persistence Modules
• Discrete Microlocal Morse Theory
• Canonical stratifications along bisheaves